'An authoritative survey with exciting new insights of special interest to economists and econometricians who analyse intertemporal and interspatial price relationships.' - Professor Angus Maddison, Groningen University This book presents a comprehensive review of recent developments in the theory and construction of index numbers using the stochastic approach, demonstrating the versatility of this approach in handling various index number problems within a single conceptual framework. It also contains a brief, but complete, review of the existing approaches to index numbers with illustrative numerical examples. The stochastic approach considers the index number problem as a signal extraction problem. The strength and reliability of the signal extracted from price and quantity changes for different commodities depends upon the messages received and the information content of the messages. The most important applications of the new approach are to be found in the context of measuring rate of inflation; fixed and chain base index numbers for temporal comparisons and for spatial intercountry comparisons; the latter generally require special index number formulae that result in transitive and base invariant comparisons.

The first edition of this book entitled Analysis on Riemannian Manifolds and Some Problems of Mathematical Physics was published by Voronezh Univer sity Press in 1989. For its English edition, the book has been substantially revised and expanded. In particular, new material has been added to Sections 19 and 20. I am grateful to Viktor L. Ginzburg for his hard work on the transla tion and for writing Appendix F, and to Tomasz Zastawniak for his numerous suggestions. My special thanks go to the referee for his valuable remarks on the theory of stochastic processes. Finally, I would like to acknowledge the support of the AMS fSU Aid Fund and the International Science Foundation (Grant NZBOOO), which made possible my work on some of the new results included in the English edition of the book. Voronezh, Russia Yuri Gliklikh September, 1995 Preface to the Russian Edition The present book is apparently the first in monographic literature in which a common treatment is given to three areas of global analysis previously consid ered quite distant from each other, namely, differential geometry and classical mechanics, stochastic differential geometry and statistical and quantum me chanics, and infinite-dimensional differential geometry of groups of diffeomor phisms and hydrodynamics. The unification of these topics under the cover of one book appears, however, quite natural, since the exposition is based on a geometrically invariant form of the Newton equation and its analogs taken as a fundamental law of motion."

The theory of Markov Decision Processes - also known under several other names including sequential stochastic optimization, discrete-time stochastic control, and stochastic dynamic programming - studies sequential optimization of discrete time stochastic systems. Fundamentally, this is a methodology that examines and analyzes a discrete-time stochastic system whose transition mechanism can be controlled over time. Each control policy defines the stochastic process and values of objective functions associated with this process. Its objective is to select a "good" control policy. In real life, decisions that humans and computers make on all levels usually have two types of impacts: (i) they cost or save time, money, or other resources, or they bring revenues, as well as (ii) they have an impact on the future, by influencing the dynamics. In many situations, decisions with the largest immediate profit may not be good in view of future events. Markov Decision Processes (MDPs) model this paradigm and provide results on the structure and existence of good policies and on methods for their calculations. MDPs are attractive to many researchers because they are important both from the practical and the intellectual points of view. MDPs provide tools for the solution of important real-life problems. In particular, many business and engineering applications use MDP models. Analysis of various problems arising in MDPs leads to a large variety of interesting mathematical and computational problems. Accordingly, the Handbook of Markov Decision Processes is split into three parts: Part I deals with models with finite state and action spaces and Part II deals with infinite state problems, and Part IIIexamines specific applications. Individual chapters are written by leading experts on the subject.

"Et moi, ... si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais poin t aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. H ea viside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service. topology has rendered mathematical physics .. .' 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d 'e1: re of this series."

This textbook gives a comprehensive introduction to stochastic processes and calculus in the fields of finance and economics, more specifically mathematical finance and time series econometrics. Over the past decades stochastic calculus and processes have gained great importance, because they play a decisive role in the modeling of financial markets and as a basis for modern time series econometrics. Mathematical theory is applied to solve stochastic differential equations and to derive limiting results for statistical inference on nonstationary processes. This introduction is elementary and rigorous at the same time. On the one hand it gives a basic and illustrative presentation of the relevant topics without using many technical derivations. On the other hand many of the procedures are presented at a technically advanced level: for a thorough understanding, they are to be proven. In order to meet both requirements jointly, the present book is equipped with a lot of challenging problems at the end of each chapter as well as with the corresponding detailed solutions. Thus the virtual text - augmented with more than 60 basic examples and 40 illustrative figures - is rather easy to read while a part of the technical arguments is transferred to the exercise problems and their solutions.

The past several years have seen the creation and extension of a very conclusive theory of statistics and probability. Many of the research workers who have been concerned with both probability and statistics felt the need for meetings that provide an opportunity for personal con tacts among scholars whose fields of specialization cover broad spectra in both statistics and probability: to discuss major open problems and new solutions, and to provide encouragement for further research through the lectures of carefully selected scholars, moreover to introduce to younger colleagues the latest research techniques and thus to stimulate their interest in research. To meet these goals, the series of Pannonian Symposia on Mathematical Statistics was organized, beginning in the year 1979: the first, second and fourth one in Bad Tatzmannsdorf, Burgenland, Austria, the third and fifth in Visegrad, Hungary. The Sixth Pannonian Symposium was held in Bad Tatzmannsdorf again, in the time between 14 and 20 September 1986, under the auspices of Dr. Heinz FISCHER, Federal Minister of Science and Research, Theodor KERY, President of the State Government of Burgenland, Dr. Franz SAUERZOPF, Vice-President of the State Govern ment of Burgenland and Dr. Josef SCHMIDL, President of the Austrian Sta tistical Central Office. The members of the Honorary Committee were Pal ERDOS, WXadisXaw ORLICZ, Pal REVESz, Leopold SCHMETTERER and Istvan VINCZE; those of the Organizing Committee were Wilfried GROSSMANN (Uni versity of Vienna), Franz KONECNY (University of Agriculture of Vienna) and, as the chairman, Wolfgang WERTZ (Technical University of Vienna)."

This book grew out of the discussions and presentations that began during the Workshop on Emerging and Reemerging Diseases (May 17-21, 1999) sponsored by the Institute for Mathematics and its Application (IMA) at the University of Minnesota with the support of NIH and NSF. The workshop started with a two-day tutorial session directed to ecologists, epidemiologists, immunologists, mathematicians, and scientists interested in the study of disease dynamics. The core of this second volume, Volume 126, covers research contributions on the use of dynamical systems (deterministic discrete, delay, PDEs, and ODEs models) and stochastic models in disease dynamics. Contributions motivated by the study of diseases like influenza, HIV, tuberculosis, and macroparasitic like schistosomiasis are also included. This second volume requires additional mathematical sophistication, and graduate students in applied mathematics, scientists in the natural, social, and health sciences, or mathematicians who want to enter the field of mathematical and theoretical epidemiology will find it useful. The collection of contributors includes many who have been in the forefront of the development of the subject.

The material of this book is based on several courses which have been delivered for a long time at the Moscow Institute for Physics and Technology. Some parts have formed the subject of lectures given at various universities throughout the world: Freie Universitat of Berlin, Chalmers University of Technology and the University of Goteborg, University of California at Santa Barbara and others. The subject of the book is the theory of queues. This theory, as a mathematical discipline, begins with the work of A. Erlang, who examined a model of a telephone station and obtained the famous formula for the distribution of the number of busy lines which is named after him. Queueing theory has been applied to the study of numerous models: emergency aid, road traffic, computer systems, etc. Besides, it has lead to several related disciplines such as reliability and inventory theories which deal with similar models. Nevertheless, many parts of the theory of queues were developed as a "pure science" with no practical applications. The aim of this book is to give the reader an insight into the mathematical methods which can be used in queueing theory and to present examples of solving problems with the help of these methods. Of course, the choice of the methods is quite subjective. Thus, many prominent results have not even been mentioned.

Aims to give to the reader the tools necessary to apply semi-Markov processes in real-life problems.

The book is self-contained and, starting from a low level of probability concepts, gradually brings the reader to a deep knowledge of semi-Markov processes.

Presents homogeneous and non-homogeneous semi-Markov processes, as well as Markov and semi-Markov rewards processes.

The concepts are fundamental for many applications, but they are not as thoroughly presented in other books on the subject as they are here.

The considerable influence of inherent uncertainties on structural behavior has led the engineering community to recognize the importance of a stochastic approach to structural problems. Issues related to uncertainty quantification and its influence on the reliability of the computational models are continuously gaining in significance. In particular, the problems of dynamic response analysis and reliability assessment of structures with uncertain system and excitation parameters have been the subject of continuous research over the last two decades as a result of the increasing availability of powerful computing resources and technology.

This book is a follow up of a previous book with the same subject (ISBN 978-90-481-9986-0) and focuses on advanced computational methods and software tools which can highly assist in tackling complex problems in stochastic dynamic/seismic analysis and design of structures. The selected chapters are authored by some of the most active scholars in their respective areas and represent some of the most recent developments in this field.

The book consists of 21 chapters which can be grouped into several thematic topics including dynamic analysis of stochastic systems, reliability-based design, structural control and health monitoring, model updating, system identification, wave propagation in random media, seismic fragility analysis and damage assessment.

This edited book is primarily intended for researchers and post-graduate students who are familiar with the fundamentals and wish to study or to advance the state of the art on a particular topic in the field of computational stochastic structural dynamics. Nevertheless, practicing engineers could benefit as well from it as most code provisions tend to incorporate probabilistic concepts in the analysis and design of structures. "

Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.

It appears that we live in an age of disasters: the mighty Missis sippi and Missouri flood millions of acres, earthquakes hit Tokyo and California, airplanes crash due to mechanical failure and the seemingly ever increasing wind speeds make the storms more and more frightening. While all these may seem to be unexpected phenomena to the man on the street, they are actually happening according to well defined rules of science known as extreme value theory. We know that records must be broken in the future, so if a flood design is based on the worst case of the past then we are not really prepared against floods. Materials will fail due to fatigue, so if the body of an aircraft looks fine to the naked eye, it might still suddenly fail if the aircraft has been in operation over an extended period of time. Our theory has by now penetrated the so cial sciences, the medical profession, economics and even astronomy. We believe that our field has come of age. In or er to fully utilize the great progress in the theory of extremes and its ever increasing acceptance in practice, an international conference was organized in which equal weight was given to theory and practice. This book is Volume I of the Proceedings of this conference. In selecting the papers for Volume lour guide was to have authoritative works with a large variety of coverage of both theory and practice."

Advances in Stochastic Modelling and Data Analysis presents the most recent developments in the field, together with their applications, mainly in the areas of insurance, finance, forecasting and marketing. In addition, the possible interactions between data analysis, artificial intelligence, decision support systems and multicriteria analysis are examined by top researchers. Audience: A wide readership drawn from theoretical and applied mathematicians, such as operations researchers, management scientists, statisticians, computer scientists, bankers, marketing managers, forecasters, and scientific societies such as EURO and TIMS.

This volume contains a large spectrum of work: super processes, Dirichlet forms, anticipative stochastic calculus, random fields and Wiener space analysis. The first part of the volume consists of two main lectures given at the third Silivri meeting in 1990: 1. "Infinitely divisible random measures and superprocesses" by D.A. Dawson, 2. "Dirichlet forms on infinite dimensional spaces and appli- cations" by M. Rockner. The second part consists of recent research papers all related to Stochastic Analysis, motivated by stochastic partial differ- ential equations, Markov fields, the Malliavin calculus and the Feynman path integrals. We would herewith like to thank the ENST for its material support for the above mentioned meeting as well as for the ini- tial preparation of this volume and to our friend and colleague Erhan Qmlar whose help and encouragement for the realization of this volume have been essential. H. Korezlioglu A. S. Ustiinel INFINITELY DIVISIBLE RANDOM MEASURES AND SUPERPROCESSES DONALD A. DAWSON 1. Introduction.

A First Course in Stochastic Calculus is a complete guide for advanced undergraduate students to take the next step in exploring probability theory and for master's students in mathematical finance who would like to build an intuitive and theoretical understanding of stochastic processes. This book is also an essential tool for finance professionals who wish to sharpen their knowledge and intuition about stochastic calculus. Louis-Pierre Arguin offers an exceptionally clear introduction to Brownian motion and to random processes governed by the principles of stochastic calculus. The beauty and power of the subject are made accessible to readers with a basic knowledge of probability, linear algebra, and multivariable calculus. This is achieved by emphasizing numerical experiments using elementary Python coding to build intuition and adhering to a rigorous geometric point of view on the space of random variables. This unique approach is used to elucidate the properties of Gaussian processes, martingales, and diffusions. One of the book's highlights is a detailed and self-contained account of stochastic calculus applications to option pricing in finance.

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. This book is devoted to stochastic operators in Hilbert space. A number of models in modern probability theory apply the notion of a stochastic operator in explicit or latent form. In this book, objects from the Gaussian case are considered. Therefore, it is useful to consider all random variables and elements as functionals from the Wiener process or its formal derivative, i.e. white noise. The book consists of five chapters. The first chapter is devoted to stochastic calculus and its main goal is to prepare the tools for solving stochastic equations. In the second chapter the structure of stochastic equations, mainly the structure of Gaussian strong linear operators, is studied. In chapter 3 the definition of the action of the stochastic operator on random elements in considered. Chapter 4 deals with the mathematical models in which the notions of stochastic calculus arise and in the final chapter the equation with random operators is considered.

Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time, renewal and regenerative processes, Poisson processes, and Brownian motion. This volume gives an in-depth description of the structure and basic properties of these stochastic processes. A main focus is on equilibrium distributions, strong laws of large numbers, and ordinary and functional central limit theorems for cost and performance parameters. Although these results differ for various processes, they have a common trait of being limit theorems for processes with regenerative increments. Extensive examples and exercises show how to formulate stochastic models of systems as functions of a system s data and dynamics, and how to represent and analyze cost and performance measures. Topics include stochastic networks, spatial and space-time Poisson processes, queueing, reversible processes, simulation, Brownian approximations, and varied Markovian models.

The technical level of the volume is between that of introductory texts that focus on highlights of applied stochastic processes, and advanced texts that focus on theoretical aspects of processes."

This textbook provides a comprehensive introduction to probability and stochastic processes, and shows how these subjects may be applied in computer performance modeling. The author's aim is to derive probability theory in a way that highlights the complementary nature of its formal, intuitive, and applicative aspects while illustrating how the theory is applied in a variety of settings. Readers are assumed to be familiar with elementary linear algebra and calculus, including being conversant with limits, but otherwise, this book provides a self-contained approach suitable for graduate or advanced undergraduate students. The first half of the book covers the basic concepts of probability, including combinatorics, expectation, random variables, and fundamental theorems. In the second half of the book, the reader is introduced to stochastic processes. Subjects covered include renewal processes, queueing theory, Markov processes, matrix geometric techniques, reversibility, and networks of queues. Examples and applications are drawn from problems in computer performance modeling. Throughout, large numbers of exercises of varying degrees of difficulty will help to secure a reader's understanding of these important and fascinating subjects.

Volume 1: (edited by Keith W. Hipel) In this landmark collection of papers, highly respected scientists and engineers from around the world present the latest research results in extreme value analyses for floods and droughts. Two approaches that are commonly employed in flood frequency analyses are the maximum annual flood and partial duration series or peak over threshold procedures. Recent theoretical advances as well as illustrative applications are described in detail for each of these approaches. Additionally, droughts and storms are systematically studied using appropriate probabilistic models. A major part of the volume is devoted to frequency analyses and fitting extreme value distributions to hydrological data. Other thought-provoking topics include regionalization techniques, distributed models, entropy and fractal analysis. Volume 1 is of interest to researchers, teachers, students and practitioners who wish to place themselves at the leading edge of flood frequency and drought analyses. Volume 2: (edited by Keith W. Hipel) World renowned scientists present valuable contributions to stochastic and statistical modelling of groundwater and surface water systems. The philosophy of probabilistic modelling in the hydrological sciences is put into proper perspective and the importance of stochastic differential equations in the environmental sciences is explained and illustrated. The new research ideas put forward in groundwater modelling will assist decision makers in tackling challenging problems such as controlling pollution of underground aquifers and obtaining adequate water supplies. Additionally, different types of stochastic models are used in modelling a range ofinteresting surface water problems. Other topics covered in this landmark volume include stochastic optimization, moment analysis, carbon dioxide modelling and rainfall prediction. Volume 2 is of interest to researchers, teachers, students and practitioners who wish to be at the leading edge of stochastic and statistical modelling in the environmental sciences. Volume 3: (edited by Keith W. Hipel; A. Ian McLeod; U.S. Panu; Vijay P. Singh) International experts from around the globe present a rich variety of intriguing developments in time series analysis in hydrology and environmental engineering. Climatic change is of great concern to everyone and significant contributions to this challenging research topic are put forward by internationally renowned authors. A range of interesting applications in hydrological forecasting are given for case studies in reservoir operation in North America, Asia and South America. Additionally, progress in entropy research is described and entropy concepts are applied to various water resource systems problems. Neural networks are employed for forecasting runoff and water demand. Moreover, graphical, nonparametric and parametric trend analyses methods are compared and applied to water quality time series. Other topics covered in this landmark volume include spatial analyses, spectral analyses and different methods for stream-flow modelling. Volume 3 constitutes an invaluable resource for researchers, teachers, students and practitioners who wish to be at the forefront of time series analysis in the environmental sciences. Volume 4: (edited by Keith W. Hipel; Liping Fang) In this landmark set of papers, experts from around the world present the latest andmost promising approaches to both the theory and practice of effective environmental management. To achieve sustainable development, organizations and individual citizens must comply with environmental laws and regulations. Accordingly, a major contribution of this book is the presentation of original techniques for designing effective environmental policies, regulations, inspection procedures and monitoring systems. Interesting methods for modelling risk and decision making problems are discussed from an environmental management perspective. Moreover, knowledge-based techniques for handling environmental problems are also investigated. Finally, the last main part of the book describes optimal approaches to reservoir operation and control that take into account appropriate multiple objectives. Volume 4 is of direct interest to researchers, teachers, students and practitioners concerned with the latest developments in environmental management and sustainable development.

Volume 1: (edited by Keith W. Hipel) In this landmark collection of papers, highly respected scientists and engineers from around the world present the latest research results in extreme value analyses for floods and droughts. Two approaches that are commonly employed in flood frequency analyses are the maximum annual flood and partial duration series or peak over threshold procedures. Recent theoretical advances as well as illustrative applications are described in detail for each of these approaches. Additionally, droughts and storms are systematically studied using appropriate probabilistic models. A major part of the volume is devoted to frequency analyses and fitting extreme value distributions to hydrological data. Other thought-provoking topics include regionalization techniques, distributed models, entropy and fractal analysis. Volume 1 is of interest to researchers, teachers, students and practitioners who wish to place themselves at the leading edge of flood frequency and drought analyses. Volume 2: (edited by Keith W. Hipel) World renowned scientists present valuable contributions to stochastic and statistical modelling of groundwater and surface water systems. The philosophy of probabilistic modelling in the hydrological sciences is put into proper perspective and the importance of stochastic differential equations in the environmental sciences is explained and illustrated. The new research ideas put forward in groundwater modelling will assist decision makers in tackling challenging problems such as controlling pollution of underground aquifers and obtaining adequate water supplies. Additionally, different types of stochastic models are used in modelling a range ofinteresting surface water problems. Other topics covered in this landmark volume include stochastic optimization, moment analysis, carbon dioxide modelling and rainfall prediction. Volume 2 is of interest to researchers, teachers, students and practitioners who wish to be at the leading edge of stochastic and statistical modelling in the environmental sciences. Volume 3: (edited by Keith W. Hipel; A. Ian McLeod; U.S. Panu; Vijay P. Singh) International experts from around the globe present a rich variety of intriguing developments in time series analysis in hydrology and environmental engineering. Climatic change is of great concern to everyone and significant contributions to this challenging research topic are put forward by internationally renowned authors. A range of interesting applications in hydrological forecasting are given for case studies in reservoir operation in North America, Asia and South America. Additionally, progress in entropy research is described and entropy concepts are applied to various water resource systems problems. Neural networks are employed for forecasting runoff and water demand. Moreover, graphical, nonparametric and parametric trend analyses methods are compared and applied to water quality time series. Other topics covered in this landmark volume include spatial analyses, spectral analyses and different methods for stream-flow modelling. Volume 3 constitutes an invaluable resource for researchers, teachers, students and practitioners who wish to be at the forefront of time series analysis in the environmental sciences. Volume 4: (edited by Keith W. Hipel; Liping Fang) In this landmark set of papers, experts from around the world present the latest andmost promising approaches to both the theory and practice of effective environmental management. To achieve sustainable development, organizations and individual citizens must comply with environmental laws and regulations. Accordingly, a major contribution of this book is the presentation of original techniques for designing effective environmental policies, regulations, inspection procedures and monitoring systems. Interesting methods for modelling risk and decision making problems are discussed from an environmental management perspective. Moreover, knowledge-based techniques for handling environmental problems are also investigated. Finally, the last main part of the book describes optimal approaches to reservoir operation and control that take into account appropriate multiple objectives. Volume 4 is of direct interest to researchers, teachers, students and practitioners concerned with the latest developments in environmental management and sustainable development.

This book discusses stochastic dynamics of power systems and the related analytical methodology. It summarizes and categorizes the stochastic elements of power systems and develops a framework for research on stochastic dynamics of power systems. It also establishes a research model for stochastic dynamics of power systems and theoretically proves stochastic stability in power systems. Further, in addition to demonstrating the stochastic oscillation mechanism in power systems, it also proposes methods for quantitative analysis and stochastic optimum control in the field of stochastic dynamic security in power systems. This book is a valuable resource for researchers, scholars and engineers in the field of electrics.

Focusing on shocks modeling, burn-in and heterogeneous populations, Stochastic Modeling for Reliability naturally combines these three topics in the unified stochastic framework and presents numerous practical examples that illustrate recent theoretical findings of the authors. The populations of manufactured items in industry are usually heterogeneous. However, the conventional reliability analysis is performed under the implicit assumption of homogeneity, which can result in distortion of the corresponding reliability indices and various misconceptions. Stochastic Modeling for Reliability fills this gap and presents the basics and further developments of reliability theory for heterogeneous populations. Specifically, the authors consider burn-in as a method of elimination of 'weak' items from heterogeneous populations. The real life objects are operating in a changing environment. One of the ways to model an impact of this environment is via the external shocks occurring in accordance with some stochastic point processes. The basic theory for Poisson shock processes is developed and also shocks as a method of burn-in and of the environmental stress screening for manufactured items are considered. Stochastic Modeling for Reliability introduces and explores the concept of burn-in in heterogeneous populations and its recent development, providing a sound reference for reliability engineers, applied mathematicians, product managers and manufacturers alike.

Most practical processes such as chemical reactor, industrial furnace, heat exchanger, etc., are nonlinear stochastic systems, which makes their con trol in general a hard problem. Currently, there is no successful design method for this class of systems in the literature. One common alterna tive consists of linearizing the nonlinear dynamical stochastic system in the neighborhood of an operating point and then using the techniques for linear systems to design the controller. The resulting model is in general an approximation of the real behavior of a dynamical system. The inclusion of the uncertainties in the model is therefore necessary and will certainly improve the performance of the dynamical system we want to control. The control of uncertain systems has attracted a lot of researchers from the control community. This topic has in fact dominated the research effort of the control community during the last two decades, and many contributions have been reported in the literature. Some practical dynamical systems have time delay in their dynamics, which makes their control a complicated task even in the deterministic case. Recently, the class ofuncertain dynamical deterministic systems with time delay has attracted some researchers, and some interesting results have been reported in both deterministic and stochastic cases. But wecan't claim that the control problem ofthis class ofsystems is completely solved; more work must be done for this class of systems."