A Weak Convergence Approach To The Theory Of Large Deviations
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A Weak Convergence Approach To The Theory Of Large Deviations
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Author : Paul Dupuis
language : en
Publisher: John Wiley & Sons
Release Date : 1997-02-27
A Weak Convergence Approach To The Theory Of Large Deviations written by Paul Dupuis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-27 with Mathematics categories.
Applies the well-developed tools of the theory of weak convergenceof probability measures to large deviation analysis--a consistentnew approach The theory of large deviations, one of the most dynamic topics inprobability today, studies rare events in stochastic systems. Thenonlinear nature of the theory contributes both to its richness anddifficulty. This innovative text demonstrates how to employ thewell-established linear techniques of weak convergence theory toprove large deviation results. Beginning with a step-by-stepdevelopment of the approach, the book skillfully guides readersthrough models of increasing complexity covering a wide variety ofrandom variable-level and process-level problems. Representationformulas for large deviation-type expectations are a key tool andare developed systematically for discrete-time problems. Accessible to anyone who has a knowledge of measure theory andmeasure-theoretic probability, A Weak Convergence Approach to theTheory of Large Deviations is important reading for both studentsand researchers.
Large Deviations And Idempotent Probability
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Author : Anatolii Puhalskii
language : en
Publisher: CRC Press
Release Date : 2001-05-07
Large Deviations And Idempotent Probability written by Anatolii Puhalskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-07 with Business & Economics categories.
In the view of many probabilists, author Anatolii Puhalskii's research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the connections between the large deviation principle (LDP) and well-known methods for establishing weak
Stochastic Differential Equations
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Author : Peter H. Baxendale
language : en
Publisher: World Scientific
Release Date : 2007
Stochastic Differential Equations written by Peter H. Baxendale and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume consists of 15 articles written by experts in stochastic analysis. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract the attention of mathematicians of all generations. Together with a short but thorough introduction to SPDEs, it presents a number of optimal, and essentially unimprovable, results about solvability for a large class of both linear and non-linear equations. The other papers in this volume were specially written for the occasion of Prof RozovskiiOCOs 60th birthday. They tackle a wide range of topics in the theory and applications of stochastic differential equations, both ordinary and with partial derivatives."
Uncertainty In Economic Theory
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Author : Itzhak Gilboa
language : en
Publisher: Routledge
Release Date : 2004-08-02
Uncertainty In Economic Theory written by Itzhak Gilboa and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-02 with Business & Economics categories.
This volume brings together important papers, coupled with new introductions, in the massively influential area of uncertainty in economic theory. Seminal papers are available together for the first time in book format, with new introductions and under the steely editorship of Itzhak Gilboa - this book is a useful reference tool for economists all over the globe.
Large Deviations For Stochastic Processes
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Author : Jin Feng
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-03
Large Deviations For Stochastic Processes written by Jin Feng and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-03 with Mathematics categories.
The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.
Stochastic Analysis And Diffusion Processes
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Author : Gopinath Kallianpur
language : en
Publisher: OUP Oxford
Release Date : 2014-01-09
Stochastic Analysis And Diffusion Processes written by Gopinath Kallianpur and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Mathematics categories.
Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.
The Logic Of Thermostatistical Physics
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Author : Gerard G. Emch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
The Logic Of Thermostatistical Physics written by Gerard G. Emch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
This book addresses several of the foundational problems in thermophysics, i. e. thermodynamics and statistical mechanics. It is an interdisciplinary work in that it examines the philosophical underpinning of scientific models and theories; it also refines the analysis of the problems at hand and delineates the place occupied by various scientific models in a generalized philosophical landscape. Hence, our philosophical - or theoretical - inquiry focuses sharply on the concept of models; and our empirical - or laboratory - evidence is sought in the model-building activities of scientists who have tried to confront the epistemological problems arising in the thermophysical sciences. Primarily for researchers and students in physics, philosophy of science, and mathematics, our book aims at informing the readers - with all the in dispensable technical details made readily available - about the nature of the foundational problems, how these problems are approached with the help of various mathematical models, and what the philosophical implications of such models and approaches involve. Some familiarity with elementary ther mophysics and/or with introductory-level philosophy of science may help, but neither is a prerequisite. The logical and mathematical background re quired for the book are introduced in the Appendices. Upon using the Subject Index, the readers may easily locate the concepts and theorems needed for understanding various parts of the book. The Citation Index lists the authors of the contributions we discuss in detail.
Biogeography
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Author : Glen MacDonald
language : en
Publisher: John Wiley & Sons
Release Date : 2002-02-28
Biogeography written by Glen MacDonald and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-02-28 with Science categories.
Biogeography illustrates how environment, space and time interact to control the large-scale distribution of organisms. This book can be used for these courses which can be offered in either department. This title includes the key concepts related to the study of vegetation and animal distributions and the human impact on these distributions.
An Introduction To Random Sets
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Author : Hung T. Nguyen
language : en
Publisher: CRC Press
Release Date : 2006-03-27
An Introduction To Random Sets written by Hung T. Nguyen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-27 with Mathematics categories.
The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis. The drawback to such diversity is that the research reports are scattered throughout the literature, with the result that i
Statistical Modeling By Wavelets
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Author : Brani Vidakovic
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-25
Statistical Modeling By Wavelets written by Brani Vidakovic and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-25 with Mathematics categories.
A comprehensive, step-by-step introduction to wavelets in statistics. What are wavelets? What makes them increasingly indispensable in statistical nonparametrics? Why are they suitable for "time-scale" applications? How are they used to solve such problems as denoising, regression, or density estimation? Where can one find up-to-date information on these newly "discovered" mathematical objects? These are some of the questions Brani Vidakovic answers in Statistical Modeling by Wavelets. Providing a much-needed introduction to the latest tools afforded statisticians by wavelet theory, Vidakovic compiles, organizes, and explains in depth research data previously available only in disparate journal articles. He carefully balances both statistical and mathematical techniques, supplementing the material with a wealth of examples, more than 100 illustrations, and extensive references-with data sets and S-Plus wavelet overviews made available for downloading over the Internet. Both introductory and data-oriented modeling topics are featured, including: * Continuous and discrete wavelet transformations. * Statistical optimality properties of wavelet shrinkage. * Theoretical aspects of wavelet density estimation. * Bayesian modeling in the wavelet domain. * Properties of wavelet-based random functions and densities. * Several novel and important wavelet applications in statistics. * Wavelet methods in time series. Accessible to anyone with a background in advanced calculus and algebra, Statistical Modeling by Wavelets promises to become the standard reference for statisticians and engineers seeking a comprehensive introduction to an emerging field.