This book presents the latest advances in the theory and practice of Marshall-Olkin distributions. These distributions have been increasingly applied in statistical practice in recent years, as they make it possible to describe interesting features of stochastic models like non-exchangeability, tail dependencies and the presence of a singular component. The book presents cutting-edge contributions in this research area, with a particular emphasis on financial and economic applications. It is recommended for researchers working in applied probability and statistics, as well as for practitioners interested in the use of stochastic models in economics. This volume collects selected contributions from the conference "Marshall-Olkin Distributions: Advances in Theory and Applications," held in Bologna on October 2-3, 2013.

Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics.
The outstanding points of these proceedings are Coherent compendium of the current state of modelling and analysis of non-linear stochastic systems from engineering, applied mathematics and physics point of view. Subject areas include: Multiscale phenomena, stability and bifurcations, control and estimation, computational methods and modelling.
For the Engineering and Physics communities, this book will provide first-hand information on recent mathematical developments. The applied mathematics community will benefit from the modelling and information on various possible applications.

The focus of this monograph is on generalizing the notion of variation in a set of numbers to variation in a set of probability distributions. The authors collect some known ways of comparing stochastic matrices in the context of information theory, statistics, economics, and population sciences. They then generalize these comparisons, introduce new comparisons, and establish the relations of implication or equivalence among sixteen of these comparisons. Some of the possible implications among these comparisons remain open questions. The results in this book establish a new field of investigation for both mathematicians and scientific users interested in the variations among multiple probability distributions. The work is divided into two parts. The first deals with finite stochastic matrices, which may be interpreted as collections of discrete probability distributions. The first part is presented in a fairly elementary mathematical setting. The introduction provides sketches of applications of concepts and methods to discrete memory-less channels in information theory, to the design and comparison of experiments in statistics, to the measurement of inequality in economics, and to various analytical problems in population genetics, ecology, and demography. Part two is more general and entails more difficult analysis involving Markov kernels. Here, many results of the first part are placed in a more general setting, as required in more sophisticated applications. A great strength of this text is the resulting connections among ideas from diverse fields: mathematics, statistics, economics, and population biology. In providing this array of new tools and concepts, the work will appeal to the practitioner. At the same time, it will serve as an excellent resource for self-study of for a graduate seminar course, as well as a stimulus to further research.

The worlds of Wall Street and The City have always held a certain allure, but in recent years have left an indelible mark on the wider public consciousness and there has been a need to become more financially literate. The quantitative nature of complex financial transactions makes them a fascinating subject area for mathematicians of all types, whether for general interest or because of the enormous monetary rewards on offer. An Introduction to Quantitative Finance concerns financial derivatives - a derivative being a contract between two entities whose value derives from the price of an underlying financial asset - and the probabilistic tools that were developed to analyse them. The theory in the text is motivated by a desire to provide a suitably rigorous yet accessible foundation to tackle problems the author encountered whilst trading derivatives on Wall Street. The book combines an unusual blend of real-world derivatives trading experience and rigorous academic background. Probability provides the key tools for analysing and valuing derivatives. The price of a derivative is closely linked to the expected value of its pay-out, and suitably scaled derivative prices are martingales, fundamentally important objects in probability theory. The prerequisite for mastering the material is an introductory undergraduate course in probability. The book is otherwise self-contained and in particular requires no additional preparation or exposure to finance. It is suitable for a one-semester course, quickly exposing readers to powerful theory and substantive problems. The book may also appeal to students who have enjoyed probability and have a desire to see how it can be applied. Signposts are given throughout the text to more advanced topics and to different approaches for those looking to take the subject further.

This book considers some models described by means of partial dif ferential equations and boundary conditions with chaotic stochastic disturbance. In a framework of stochastic Partial Differential Equa tions an approach is suggested to generalize solutions of stochastic Boundary Problems. The main topic concerns probabilistic aspects with applications to well-known Random Fields models which are representative for the corresponding stochastic Sobolev spaces. {The term "stochastic" in general indicates involvement of appropriate random elements. ) It assumes certain knowledge in general Analysis and Probability {Hilbert space methods, Schwartz distributions, Fourier transform) . I A very general description of the main problems considered can be given as follows. Suppose, we are considering a random field ~ in a region T ~ Rd which is associated with a chaotic (stochastic) source"' by means of the differential equation (*) in T. A typical chaotic source can be represented by an appropri ate random field"' with independent values, i. e. , generalized random function"' = ( cp, 'TJ), cp E C~(T), with independent random variables ( cp, 'fJ) for any test functions cp with disjoint supports. The property of having independent values implies a certain "roughness" of the ran dom field "' which can only be treated functionally as a very irregular Schwarz distribution. With the lack of a proper development of non linear analyses for generalized functions, let us limit ourselves to the 1 For related material see, for example, J. L. Lions, E.

In recent years, as part of the increasing "informationization" of industry and the economy, enterprises have been accumulating vast amounts of detailed data such as high-frequency transaction data in nancial markets and point-of-sale information onindividualitems in theretail sector. Similarly,vast amountsof data arenow ava- able on business networks based on inter rm transactions and shareholdings. In the past, these types of information were studied only by economists and management scholars. More recently, however, researchers from other elds, such as physics, mathematics, and information sciences, have become interested in this kind of data and, based on novel empirical approaches to searching for regularities and "laws" akin to those in the natural sciences, have produced intriguing results. This book is the proceedings of the international conference THICCAPFA7 that was titled "New Approaches to the Analysis of Large-Scale Business and E- nomic Data," held in Tokyo, March 1-5, 2009. The letters THIC denote the Tokyo Tech (Tokyo Institute of Technology)-Hitotsubashi Interdisciplinary Conference. The conference series, titled APFA (Applications of Physics in Financial Analysis), focuses on the analysis of large-scale economic data. It has traditionally brought physicists and economists together to exchange viewpoints and experience (APFA1 in Dublin 1999, APFA2 in Liege ` 2000, APFA3 in London 2001, APFA4 in Warsaw 2003, APFA5 in Torino 2006, and APFA6 in Lisbon 2007). The aim of the conf- ence is to establish fundamental analytical techniques and data collection methods, taking into account the results from a variety of academic disciplines.

This text is an Elementary Introduction to Stochastic Processes in discrete and continuous time with an initiation of the statistical inference. The material is standard and classical for a first course in Stochastic Processes at the senior/graduate level (lessons 1-12). To provide students with a view of statistics of stochastic processes, three lessons (13-15) were added. These lessons can be either optional or serve as an introduction to statistical inference with dependent observations. Several points of this text need to be elaborated, (1) The pedagogy is somewhat obvious. Since this text is designed for a one semester course, each lesson can be covered in one week or so. Having in mind a mixed audience of students from different departments (Math ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on moti vation of concepts, aspects of applications and computational procedures. Basically, we try to explain to beginners questions such as "What is the topic in this lesson?" "Why this topic?," "How to study this topic math ematically?." The exercises at the end of each lesson will deepen the stu dents' understanding of the material, and test their ability to carry out basic computations. Exercises with an asterisk are optional (difficult) and might not be suitable for homework, but should provide food for thought."

Strategies for Quasi-Monte Carlo builds a framework to design and analyze strategies for randomized quasi-Monte Carlo (RQMC). One key to efficient simulation using RQMC is to structure problems to reveal a small set of important variables, their number being the effective dimension, while the other variables collectively are relatively insignificant. Another is smoothing. The book provides many illustrations of both keys, in particular for problems involving Poisson processes or Gaussian processes. RQMC beats grids by a huge margin. With low effective dimension, RQMC is an order-of-magnitude more efficient than standard Monte Carlo. With, in addition, certain smoothness - perhaps induced - RQMC is an order-of-magnitude more efficient than deterministic QMC. Unlike the latter, RQMC permits error estimation via the central limit theorem. For random-dimensional problems, such as occur with discrete-event simulation, RQMC gets judiciously combined with standard Monte Carlo to keep memory requirements bounded. This monograph has been designed to appeal to a diverse audience, including those with applications in queueing, operations research, computational finance, mathematical programming, partial differential equations (both deterministic and stochastic), and particle transport, as well as to probabilists and statisticians wanting to know how to apply effectively a powerful tool, and to those interested in numerical integration or optimization in their own right. It recognizes that the heart of practical application is algorithms, so pseudocodes appear throughout the book. While not primarily a textbook, it is suitable as a supplementary text for certain graduate courses. As a reference, it belongs on the shelf of everyone with a serious interest in improving simulation efficiency. Moreover, it will be a valuable reference to all those individuals interested in improving simulation efficiency with more than incremental increases.

Probability theory on compact Lie groups deals with the interaction between chance and symmetry, a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications.

The book is primarily aimed at researchers working in probability, stochastic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists, statisticians and engineers who are working on related applications. A background in first year graduate level measure theoretic probability and functional analysis is essential; a background in Lie groups and representation theory is certainly helpful but the first two chapters also offer orientation in these subjects."

This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries Functional equations in hypergroups Stability of functional equations Fischer-Muszely equation Haar meager sets and Haar null sets Dynamical systems Functional equations in probability theory Stochastic convex ordering Dhombres functional equation Nonstandard analysis and Ulam stability This book is dedicated in memory of Stanilsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.

Statistics is strongly tied to applications in different scientific disciplines, and the most challenging statistical problems arise from problems in the sciences. In fact, the most innovative statistical research flows from the needs of applications in diverse settings. This volume is a testimony to the crucial role that statistics plays in scientific disciplines such as genetics and environmental sciences, among others. The articles in this volume range from human and agricultural genetic DNA research to carcinogens and chemical concentrations in the environment and to space debris and atmospheric chemistry. Also included are some articles on statistical methods which are sufficiently general and flexible to be applied to many practical situations. The papers were refereed by a panel of experts and the editors of the volume. The contributions are based on the talks presented at the Workshop on Statistics and the Sciences, held at the Centro Stefano Franscini in Ascona, Switzerland, during the week of May 23 to 28, 1999. The meeting was jointly organized by the Swiss Federal Institutes of Technology in Lausanne and Zurich, with the financial support of the Minerva Research Foundation. As the presentations at the workshop helped the participants recognize the po tential role that statistics can play in the sciences, we hope that this volume will help the reader to focus on the central role of statistics in the specific areas presented here and to extrapolate the results to further applications."

The purpose of this textbook is to bring together, in a self-contained introductory form, the scattered material in the field of stochastic processes and statistical physics. It offers the opportunity of being acquainted with stochastic, kinetic and nonequilibrium processes. Although the research techniques in these areas have become standard procedures, they are not usually taught in the normal courses on statistical physics. For students of physics in their last year and graduate students who wish to gain an invaluable introduction on the above subjects, this book is a necessary tool.

Lagrangian expansions can be used to obtain numerous very useful probability models, which have been applied to real life situations including, but not limited to branching processes, queuing processes, stochastic processes, environmental toxicology, diffusion of information, ecology, strikes in industries, sales of new products, and amount of production for optimum profits. This book is a comprehensive, systematic treatment of the two classes of Lagrangian probability distributions along with some of their sub-families and their properties; important applications are also given.Graduate students and researchers interested in Lagrangian probability distributions, who have sound knowledge of standard statistical techniques, will find this book valuable. It may be used as a reference text or in courses and seminars on distribution theory and Lagrangian distributions. Applied scientists and researchers in environmental statistics, reliability, sales management, epidemiology, operations research, and the optimization of profits in manufacturing and marketing will benefit immensely from the various applications in the book.

The ability to effective learn, process, and retain new information is critical to the success of any student. Since mathematics are becoming increasingly more important in our educational systems, it is imperative that we devise an efficient system to measure these types of information recall. Assessing and Measuring Statistics Cognition in Higher Education Online Environments: Emerging Research and Opportunities is a critical reference source that overviews the current state of higher education learning assessment systems. Featuring extensive coverage on relevant topics such as statistical cognitions, online learning implications, cognitive development, and curricular mismatches, this publication is ideally designed for academics, students, educators, professionals, and researchers seeking innovative perspectives on current assessment and measurement systems within our educational facilities.

During the 1980s, the use of log-linear statistical models in behavioral and life-science inquiry increased markedly. Concurrently, log-linear theory, developed largely during the previous decade, has been streamlined and refined. An aim of this second edition is to acquaint old and new readers with these refinements. The most significant change that has occurred is the increased availability of user-oriented computer programs for the performance of log-linear analyses. During this period, all major statistical packages (i.e., BMDP, SAS, and SPSS) introduced either new or improved computer programs designed specifically for the specification and fitting of log-linear models. Consequently, the enhanced ability of practicing researchers to perform log-linear analyses has been accompanied by an enhanced need for didactic explanations of this system of analysis--for explanations of log-linear theory and method that can be readily understood by practitioners and graduate students who do not possess recondite backgrounds in mathematical statistics, yet who desire to obtain a level of understanding beyond that which is typically offered by cookbook approaches to statistical topics. Another aim of this second edition is to fulfill this need.

As before, this edition has been prepared for readers who have had at least one intermediate-level course in applied statistics in which the basic principles of factorial analysis of variance and multiple regression were discussed. Also as before, to assist readers with modest preparation in the analysis of quantitative/categorical data, this edition will review topics in such relevant areas as basic probability theory, traditional chi-square goodness-of-fit procedures, and the method of maximum-likelihood estimation. Readers with strong backgrounds in statistics can skim over these preparatory discussions, contained largely in Chapters 2 and 3, without prejudice.

This book provides a comprehensive summary of a wide variety of statistical methods for the analysis of repeated measurements. It is designed to be both a useful reference for practitioners and a textbook for a graduate-level course focused on methods for the analysis of repeated measurements. This book will be of interest to * Statisticians in academics, industry, and research organizations * Scientists who design and analyze studies in which repeated measurements are obtained from each experimental unit * Graduate students in statistics and biostatistics. The prerequisites are knowledge of mathematical statistics at the level of Hogg and Craig (1995) and a course in linear regression and ANOVA at the level of Neter et. al. (1985). The important features of this book include a comprehensive coverage of classical and recent methods for continuous and categorical outcome variables; numerous homework problems at the end of each chapter; and the extensive use of real data sets in examples and homework problems. The 80 data sets used in the examples and homework problems can be downloaded from www.springer-ny.com at the list of author websites. Since many of the data sets can be used to demonstrate multiple methods of analysis, instructors can easily develop additional homework problems and exam questions based on the data sets provided. In addition, overhead transparencies produced using TeX and solutions to homework problems are available to course instructors. The overheads also include programming statements and computer output for the examples, prepared primarily using the SAS System. Charles S. Davis is Senior Director of Biostatistics at Elan Pharmaceuticals, San Diego, California. He previously was professor in the Department of Biostatistics at the University of Iowa. He is author or co-author of more than 75 peer-reviewed papers in statistical and medical journals and one book (Categorical Data Analysis using the SAS System with Maura Stokes and Gary Koch). His research and teaching interests include categorical data analysis, methods for the analysis of repeated measurements, and clinical trials. Dr. Davis has consulted with numerous companies and has taught short courses on categorical data analysis, methods for the analysis of repeated measurements, and clinical trials methodology for industrial, government, and academic organizations. He received an "Excellence in Continuing Education" award from the American Statistical Association in 2001 and has served as associate editor of the journals Controlled Clinical Trials and The American Statistician and as chair of the Biometrics Section of the ASA.

This book contains a rich set of tools for nonparametric analyses, and the purpose of this text is to provide guidance to students and professional researchers on how R is used for nonparametric data analysis in the biological sciences: To introduce when nonparametric approaches to data analysis are appropriate To introduce the leading nonparametric tests commonly used in biostatistics and how R is used to generate appropriate statistics for each test To introduce common figures typically associated with nonparametric data analysis and how R is used to generate appropriate figures in support of each data set The book focuses on how R is used to distinguish between data that could be classified as nonparametric as opposed to data that could be classified as parametric, with both approaches to data classification covered extensively. Following an introductory lesson on nonparametric statistics for the biological sciences, the book is organized into eight self-contained lessons on various analyses and tests using R to broadly compare differences between data sets and statistical approach.

This volume is based on lectures notes for the courses delivered at the Cimpa Summer School: From Classical to Modern Probability, held at Temuco, Chile, be th th tween January 8 and 26, 2001. This meeting brought together probabilists and graduate students interested in fields like particle systems, percolation, Brownian motion, random structures, potential theory and stochastic processes. We would like to express our gratitude to all the participants of the school as well as the people who contributed to its organization. In particular, to Servet Martinez, and Pablo Ferrari for their scientific advice, and Cesar Burgueiio for all his support and friendship. We want to thank all the professors for their stimulating courses and lectures. Special thanks to those who took the extra work in preparing each chapter of this book. We are also indebted to our sponsors and supporting institutions, whose interest and help was essential to organize this meeting: CIMPA, CNRS, CONI CYT, ECOS, FONDAP Program in Applied Mathematics, French Cooperation, Fundacion Andes, Presidential Fellowship, Universidad de Chile and Universidad de La Frontera. We are grateful to Miss Gladys Cavallone for her excellent work during the preparation of the meeting as well as for the considerable task of unifying the typography of the different chapters of this book."

Extending the well-known connection between classical linear potential theory and probability theory (through the interplay between harmonic functions and martingales) to the nonlinear case of tug-of-war games and their related partial differential equations, this unique book collects several results in this direction and puts them in an elementary perspective in a lucid and self-contained fashion.

The classical optimal control theory deals with the determination of an optimal control that optimizes the criterion subjects to the dynamic constraint expressing the evolution of the system state under the influence of control variables. If this is extended to the case of multiple controllers (also called players) with different and sometimes conflicting optimization criteria (payoff function) it is possible to begin to explore differential games. Zero-sum differential games, also called differential games of pursuit, constitute the most developed part of differential games and are rigorously investigated. In this book, the full theory of differential games of pursuit with complete and partial information is developed. Numerous concrete pursuit-evasion games are solved ("life-line" games, simple pursuit games, etc.), and new time-consistent optimality principles in the n-person differential game theory are introduced and investigated.

This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is "white," i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.

A critical yet constructive description of the rich analytical techniques and substantive applications that typify how statistical thinking has been applied at the RAND Corporation over the past two decades. Case studies of public policy problems are useful for teaching because they are familiar: almost everyone knows something abut health insurance, global warming, and capital punishment, to name but a few of the applications covered in this casebook. Each case study has a common format that describes the policy questions, the statistical questions, and the successful and the unsuccessful analytic strategies. Readers should be familiar with basic statistical concepts including sampling and regression. While designed for statistics courses in areas ranging from economics to health policy to the law at both the advanced undergraduate and graduate levels, empirical researchers and policy-makers will also find this casebook informative.

This book deals with the impact of uncertainty in input data on the outputs of mathematical models. Uncertain inputs as scalars, tensors, functions, or domain boundaries are considered. In practical terms, material parameters or constitutive laws, for instance, are uncertain, and quantities as local temperature, local mechanical stress, or local displacement are monitored. The goal of the worst scenario method is to extremize the quantity over the set of uncertain input data.
A general mathematical scheme of the worst scenario method, including approximation by finite element methods, is presented, and then applied to various state problems modeled by differential equations or variational inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, plate buckling, contact problems in elasticity and thermoelasticity with and without friction, and various models of plastic deformation, to list some of the topics. Dozens of examples, figures, and tables are included.
Although the book concentrates on the mathematical aspects of the subject, a substantial part is written in an accessible style and is devoted to various facets of uncertainty in modeling and to the state of the art techniques proposed to deal with uncertain input data.
A chapter on sensitivity analysis and on functional and convex analysis is included for the reader's convenience.
-Rigorous theory is established for the treatment of uncertainty in modeling
- Uncertainty is considered in complex models based on partial differential equations or variational inequalities
- Applications to nonlinear and linear problems with uncertain data are presented in detail: quasilinear steady heat flow, buckling of beams and plates, vibration of beams, frictional contact of bodies, several models of plastic deformation, and more
-Although emphasis is put on theoretical analysis and approximation techniques, numerical examples are also present
-Main ideas and approaches used today to handle uncertainties in modeling are described in an accessible form
-Fairly self-contained book

The subject theory is important in finance, economics, investment strategies, health sciences, environment, industrial engineering, etc.