Markov Processes From K It S Perspective

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Markov Processes From K It S Perspective

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Author : Daniel W. Stroock
language : en
Publisher: Princeton University Press
Release Date : 2003-05-26

Markov Processes From K It S Perspective written by Daniel W. Stroock and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-26 with Mathematics categories.

Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes.

Nonlinear Markov Processes And Kinetic Equations

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Author : Vassili N. Kolokoltsov
language : en
Publisher: Cambridge University Press
Release Date : 2010-07-15

Nonlinear Markov Processes And Kinetic Equations written by Vassili N. Kolokoltsov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-15 with Mathematics categories.

A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.

Perspectives Of Systems Informatics

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Author : Amir Pnueli
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-08

Perspectives Of Systems Informatics written by Amir Pnueli 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 2010-02-08 with Computers categories.

This book contains thoroughly refereed and revised papers from the 7th International Andrei Ershov Memorial Conference on Perspectives of System Informatics, PSI 2009, held in Akademgorodok, Novosibirsk, Russia, in June 2009. The 26 revised full papers and 4 revised short papers presented were carefully reviewed and selected from 67 submissions. The volume also contains 5 invited papers covering a range of hot topics in system informatics. The papers address all current aspects of theoretical computer science, programming methodology, and new information technologies, which are among the most important contributions of system informatics.

Markov Chains And Stochastic Stability

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Author : Sean Meyn
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-02

Markov Chains And Stochastic Stability written by Sean Meyn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-02 with Mathematics categories.

Meyn and Tweedie is back! The bible on Markov chains in general state spaces has been brought up to date to reflect developments in the field since 1996 - many of them sparked by publication of the first edition. The pursuit of more efficient simulation algorithms for complex Markovian models, or algorithms for computation of optimal policies for controlled Markov models, has opened new directions for research on Markov chains. As a result, new applications have emerged across a wide range of topics including optimisation, statistics, and economics. New commentary and an epilogue by Sean Meyn summarise recent developments and references have been fully updated. This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.

Mathematics Of The Bond Market A L Vy Processes Approach

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Author : Michał Barski
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-23

Mathematics Of The Bond Market A L Vy Processes Approach written by Michał Barski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-23 with Business & Economics categories.

Analyses bond market models with Lévy stochastic factors, suitable for graduates and researchers in probability and mathematical finance.

Mathematical Perspectives On Neural Networks

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Author : Paul Smolensky
language : en
Publisher: Psychology Press
Release Date : 2013-05-13

Mathematical Perspectives On Neural Networks written by Paul Smolensky and has been published by Psychology Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-13 with Psychology categories.

Recent years have seen an explosion of new mathematical results on learning and processing in neural networks. This body of results rests on a breadth of mathematical background which even few specialists possess. In a format intermediate between a textbook and a collection of research articles, this book has been assembled to present a sample of these results, and to fill in the necessary background, in such areas as computability theory, computational complexity theory, the theory of analog computation, stochastic processes, dynamical systems, control theory, time-series analysis, Bayesian analysis, regularization theory, information theory, computational learning theory, and mathematical statistics. Mathematical models of neural networks display an amazing richness and diversity. Neural networks can be formally modeled as computational systems, as physical or dynamical systems, and as statistical analyzers. Within each of these three broad perspectives, there are a number of particular approaches. For each of 16 particular mathematical perspectives on neural networks, the contributing authors provide introductions to the background mathematics, and address questions such as: * Exactly what mathematical systems are used to model neural networks from the given perspective? * What formal questions about neural networks can then be addressed? * What are typical results that can be obtained? and * What are the outstanding open problems? A distinctive feature of this volume is that for each perspective presented in one of the contributed chapters, the first editor has provided a moderately detailed summary of the formal results and the requisite mathematical concepts. These summaries are presented in four chapters that tie together the 16 contributed chapters: three develop a coherent view of the three general perspectives -- computational, dynamical, and statistical; the other assembles these three perspectives into a unified overview of the neural networks field.

Nonlinear Mixture Models A Bayesian Approach

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Author : Tatiana V Tatarinova
language : en
Publisher: World Scientific
Release Date : 2014-12-30

Nonlinear Mixture Models A Bayesian Approach written by Tatiana V Tatarinova and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-30 with Mathematics categories.

This book, written by two mathematicians from the University of Southern California, provides a broad introduction to the important subject of nonlinear mixture models from a Bayesian perspective. It contains background material, a brief description of Markov chain theory, as well as novel algorithms and their applications. It is self-contained and unified in presentation, which makes it ideal for use as an advanced textbook by graduate students and as a reference for independent researchers. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.In this book the authors present Bayesian methods of analysis for nonlinear, hierarchical mixture models, with a finite, but possibly unknown, number of components. These methods are then applied to various problems including population pharmacokinetics and gene expression analysis. In population pharmacokinetics, the nonlinear mixture model, based on previous clinical data, becomes the prior distribution for individual therapy. For gene expression data, one application included in the book is to determine which genes should be associated with the same component of the mixture (also known as a clustering problem). The book also contains examples of computer programs written in BUGS. This is the first book of its kind to cover many of the topics in this field.

Intelligent Agents Ii Agent Theories Architectures And Languages

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Author : Michael J. Wooldridge
language : en
Publisher: Springer Science & Business Media
Release Date : 1996

Intelligent Agents Ii Agent Theories Architectures And Languages written by Michael J. Wooldridge 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 1996 with Artificial intelligence categories.

This book is based on the second International Workshop on Agent Theories, Architectures, and Languages, held in conjunction with the International Joint Conference on Artificial Intelligence, IJCAI'95 in Montreal, Canada in August 1995. The 26 papers are revised final versions of the workshop presentations selected from a total of 54 submissions; also included is a comprehensive introduction, a detailed bibliography listing 355 relevant publications, and a subject index. The book is structured into seven sections, reflecting the most current major directions in agent-related research. Together with its predecessor, Intelligent Agents, published as volume 890 in the LNAI series, this book provides a timely and comprehensive state-of-the-art report.

Analogical Reasoning

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Author : D.H. Helman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Analogical Reasoning written by D.H. Helman 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 2013-06-29 with Philosophy categories.

In the last few years, there has been an enormous amount of activity in the study of analogy and metaphor. This is partly because of an interest of artificial intelligence researchers in simulating learning processes using analogy. It also arises from critical examinations of standard theories in the philosophy of language, with their inbuilt literal/meta phoric distinction. This volume consists of recent previously unpub lished work in this area, with a particular emphasis upon the role of analogies in reasoning and, more generally, their role in thought and language. The papers are contributed by philosophers, computer scientists, cognitive scientists and literary critics. Researchers in these fields whose focus is the study of analogy and metaphor will find much of interest in this volume. These essays can also serve as an introduction to some of the major approaches taken in the investigation of analogy. As noted, this volume brings together the work of researchers in several different disciplines. The various approaches taken with respect to the understanding of analogy tend to be rather different, however, the articles suggest a common conclusion. Analogy and metaphor pervade thought and language; their close investigation thus constitutes a valuable contribution to our understanding of persons. DAVID H. HELMAN Case Western Reserve University vii PART I CONCEPTUAL AND CATEGORICAL THEORIES OF ANALOGICAL UNDERSTANDING MARK TURNER CATEGORIES AND ANALOGIES I want to pursue the following claims: The way we categorize helps explain the way we recognize a statement as an analogy.

Stochastic Partial Differential Equations Six Perspectives

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Author : René Carmona
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Stochastic Partial Differential Equations Six Perspectives written by René Carmona 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 1999 with Mathematics categories.

Presents the main topics of interest in the field of stochastic partial differential equations (SPDEs), emphasizing breakthroughs and such basic issues as the role of SPDEs in stochastic modeling, how SPDEs arise, and how their theory is applied in different disciplines. Emphasis is placed on the genesis and applications of SPDEs, as well as mathematical theory and numerical methods. Suitable for graduate level students, researchers. Annotation copyrighted by Book News, Inc., Portland, OR