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.

Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have been developed to formulate these problems theoretically and then to solve them either exactly or approximately.

This book aims to gather a collection of papers dealing with several different problems arising from many disciplines and some modern mathematical approaches to handle them. In this respect, the book offers a wide overview on many of the current trends in Mathematics as valuable formal techniques in capturing and exploiting the complexity involved in real-world situations.

Several researchers, colleagues, friends and students of Professor Maria Luisa Menendez have contributed to this volume to pay tribute to her and to recognize the diverse contributions she had made to the fields of Mathematics and Statistics and to the profession in general. She had a sweet and strong personality, and instilled great values and work ethics in her students through her dedication to teaching and research. Even though the academic community lost her prematurely, she would continue to provide inspiration to many students and researchers worldwide through her published work."

Quantum groups have been investigated rather deeply in mathematical physics over the last decade. Among the most prominent contributions in this area let us mention the works of V.G. Drinfeld, S.L. Woronowicz, S. Majid. Prob ability the- ory on quantum groups has developed in several directions (see works of P. Biane, RL. Hudson and K.R Partasarathy, P.A. Meyer, M. Schurmann, D. Voiculescu). The aim of this book is to present several new aspects related to quantum groups: operator calculus, dual representations, stochastic processes and diffusions, Appell polynomials and systems in connection with evolution equations. Much of the ma- terial is scattered throughout available literature, however, we have nowhere found in accessible form all of this material collected. The presentation of representation theory in connection with Appell systems is original with the authors. Stochastic processes (example: Brownian motion, diffusion processes, Levy processes) are in- vestigated and several examples are presented. As a text the work is intended to be accessible to graduate students and researchers not specialised in quantum prob ability. We would like to acknowledge our colleagues P. Feinsilver, R Lenzceswki, D.

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.

Networks can provide a useful model and graphic image useful for the description of a wide variety of web-like structures in the physical and man-made realms, e.g. protein networks, food webs and the Internet. The contributions gathered in the present volume provide both an introduction to, and an overview of, the multifaceted phenomenology of complex networks. Statistical Mechanics of Complex Networks also provides a state-of-the-art picture of current theoretical methods and approaches.

This book explores all relevant aspects of net scoring, also known as uplift modeling: a data mining approach used to analyze and predict the effects of a given treatment on a desired target variable for an individual observation. After discussing modern net score modeling methods, data preparation, and the assessment of uplift models, the book investigates software implementations and real-world scenarios. Focusing on the application of theoretical results and on practical issues of uplift modeling, it also includes a dedicated chapter on software solutions in SAS, R, Spectrum Miner, and KNIME, which compares the respective tools. This book also presents the applications of net scoring in various contexts, e.g. medical treatment, with a special emphasis on direct marketing and corresponding business cases. The target audience primarily includes data scientists, especially researchers and practitioners in predictive modeling and scoring, mainly, but not exclusively, in the marketing context.

Edexcel and A Level Modular Mathematics S2 features: Student-friendly worked examples and solutions, leading up to a wealth of practice questions. Sample exam papers for thorough exam preparation. Regular review sections consolidate learning. Opportunities for stretch and challenge presented throughout the course. 'Escalator section' to step up from GCSE. PLUS Free LiveText CD-ROM, containing Solutionbank and Exam Cafe to support, motivate and inspire students to reach their potential for exam success. Solutionbank contains fully worked solutions with hints and tips for every question in the Student Books. Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary.

This work supplies the reader with formulas, maps out the procedure to follow, and provides working charts, tables, and calculating machines to allow the reader to compute statistics for application to problems in psychology and education.

Spatial statistics are useful in subjects as diverse as climatology, ecology, economics, environmental and earth sciences, epidemiology, image analysis and more. This book covers the best-known spatial models for three types of spatial data: geostatistical data (stationarity, intrinsic models, variograms, spatial regression and space-time models), areal data (Gibbs-Markov fields and spatial auto-regression) and point pattern data (Poisson, Cox, Gibbs and Markov point processes). The level is relatively advanced, and the presentation concise but complete.

The most important statistical methods and their asymptotic properties are described, including estimation in geostatistics, autocorrelation and second-order statistics, maximum likelihood methods, approximate inference using the pseudo-likelihood or Monte-Carlo simulations, statistics for point processes and Bayesian hierarchical models. A chapter is devoted to Markov Chain Monte Carlo simulation (Gibbs sampler, Metropolis-Hastings algorithms and exact simulation).
A large number of real examples are studied with R, and each chapter ends with a set of theoretical and applied exercises. While a foundation in probability and mathematical statistics is assumed, three appendices introduce some necessary background. The book is accessible to senior undergraduate students with a solid math background and Ph.D. students in statistics. Furthermore, experienced statisticians and researchers in the above-mentioned fields will find the book valuable as a mathematically sound reference.

This book is the English translation of Modelisation et Statistique Spatiales published by Springer in the series Mathematiques & Applications, a series established by Societe de Mathematiques Appliquees et Industrielles (SMAI)."

Probability is relevant to so many different subject areas that its importance as a mathematical technique cannot be underestimated. This book provides a comprehensive, user-friendly introduction to the subject. The step-by-step approach taken by the author allows students to develop knowledge at their own pace and, by working through the numerous exercises, they are ensured a full understanding of the material before moving on to more advanced sections. Traditional examples of probablistic theory, such as coins and dice, are included but the author has also used many exercises based on real-life problems. The result is an introduction to probability that avoids the overly confusing, theoretical approach often adopted in this area, and provides a simple and concise text that will be invaluable to all studying first and second year courses on the subject.

This book contains selected contributions from the geoENV98 - the Second European Conference on Geostatistics for Environmental Sciences, held in Valencia, Spain in November 1998. This second book of the geoENV series illustrates the developments on geostatistics as applied to the environmental sciences which have occurred during the past two years. It also presents practical applications which will be of interest to both researchers and practitioners. The book starts with three keynote papers on ecology, climatology and soil science, followed by forty-three contributions. The contents of the book are eminently practical. The objective of the editors was to compile a set of papers in which the reader could perceive how geostatistics is applied within the environmental sciences. A few selected theoretical contributions are also included. The papers are organized in the following seven main areas Air pollution Climatology Ecology Hydrogeology Soil Science Theory Other applications presenting applications varying from particle matter analysis, noise exposure sampling, space-time modeling of ozone levels, downscaling of precipitation, kriging with categorical external drift, analysis of fish abundance, combining variograms and radio-telemetry in ecology, kriging radionuclide deposition, mapping of soil contamination, network design for soil monitoring, inverse modeling in hydrogeology, groundwater transport modeling, coastal evolution mapping to spatial modeling of cancer ratios. Audience: This publication will be of great interest and practical value to geostatisticians working both in academia and in industry.

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 volume of the Encyclopaedia is a survey of stochastic calculus, an increasingly important part of probability, authored by well-known experts in the field. The book addresses graduate students and researchers in probability theory and mathematical statistics, as well as physicists and engineers who need to apply stochastic methods.

The aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer science, mathematical physics and finance. Each chapter contains didactical material as well as more advanced technical sections. Few appendices will help refreshing memories (if necessary!).
. New probabilistic model, new results in probability theory
. Original applications in computer science
. Applications in mathematical physics
. Applications in finance

This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSN097) which was held in Ischia, Italy, in June 1997. The rapid progress of computer technologies, including new parallel architec tures, has stimulated a large amount of research devoted to building software environments and defining algorithms able to fully exploit this new computa tional power. In some sense, numerical analysis has to conform itself to the new tools. The impact of parallel computing in nonlinear optimization, which had a slow start at the beginning, seems now to increase at a fast rate, and it is reasonable to expect an even greater acceleration in the future. As with the first HPSNO conference, the goal of the HPSN097 conference was to supply a broad overview of the more recent developments and trends in nonlinear optimization, emphasizing the algorithmic and high performance software aspects. Bringing together new computational methodologies with theoretical ad vances and new computer technologies is an exciting challenge that involves all scientists willing to develop high performance numerical software. This book contains several important contributions from different and com plementary standpoints. Obviously, the articles in the book do not cover all the areas of the conference topic or all the most recent developments, because of the large number of new theoretical and computational ideas of the last few years."

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.

This book prepares students to execute the quantitative and computational needs of the finance industry. The quantitative methods are explained in detail with examples from real financial problems like option pricing, risk management, portfolio selection, etc. Codes are provided in R programming language to execute the methods. Tables and figures, often with real data, illustrate the codes. References to related work are intended to aid the reader to pursue areas of specific interest in further detail. The comprehensive background with economic, statistical, mathematical, and computational theory strengthens the understanding. The coverage is broad, and linkages between different sections are explained. The primary audience is graduate students, while it should also be accessible to advanced undergraduates. Practitioners working in the finance industry will also benefit.

This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10-14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Roeckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker-Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.

In response to a growing interest in Total Least Squares (TLS) and Errors-In-Variables (EIV) modeling by researchers and practitioners, well-known experts from several disciplines were invited to prepare an overview paper and present it at the third international workshop on TLS and EIV modeling held in Leuven, Belgium, August 27-29, 2001. These invited papers, representing two-thirds of the book, together with a selection of other presented contributions yield a complete overview of the main scientific achievements since 1996 in TLS and Errors-In-Variables modeling. In this way, the book nicely completes two earlier books on TLS (SIAM 1991 and 1997). Not only computational issues, but also statistical, numerical, algebraic properties are described, as well as many new generalizations and applications. Being aware of the growing interest in these techniques, it is a strong belief that this book will aid and stimulate users to apply the new techniques and models correctly to their own practical problems.

tEL moi, .., ' si favait su comment en revenir. je One service mathematics has rendered the n 'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled' discarded nonsense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics .. .'; 'One service logic has rendered computer science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series."

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 book gives a comprehensive overview of modern non-life actuarial science. It starts with a verbal description (i.e. without using mathematical formulae) of the main actuarial problems to be solved in non-life practice. Then in an extensive second chapter all the mathematical tools needed to solve these problems are dealt with - now in mathematical notation. The rest of the book is devoted to the exact formulation of various problems and their possible solutions. Being a good mixture of practical problems and their actuarial solutions, the book addresses above all two types of readers: firstly students (of mathematics, probability and statistics, informatics, economics) having some mathematical knowledge, and secondly insurance practitioners who remember mathematics only from some distance. Prerequisites are basic calculus and probability theory.