Semigroups Boundary Value Problems And Markov Processes
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Semigroups Boundary Value Problems And Markov Processes
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Author : Kazuaki Taira
language : en
Publisher: Springer
Release Date : 2014-08-07
Semigroups Boundary Value Problems And Markov Processes written by Kazuaki Taira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-07 with Mathematics categories.
A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes and Comments where bibliographical references are primarily discussed. Thanks to the kind feedback from many readers, some errors in the first edition have been corrected. In order to keep the book up-to-date, new references have been added to the bibliography. Researchers and graduate students interested in PDEs, functional analysis and probability will find this volume useful.
Boundary Value Problems And Markov Processes
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Author : Kazuaki Taira
language : en
Publisher: Springer
Release Date : 2009-06-17
Boundary Value Problems And Markov Processes written by Kazuaki Taira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-17 with Mathematics categories.
This is a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel’ boundary conditions in probability theory. It presents new developments in the theory of singular integrals.
Boundary Value Problems And Markov Processes
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Author : Kazuaki Taira
language : en
Publisher:
Release Date : 2020
Boundary Value Problems And Markov Processes written by Kazuaki Taira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Boundary value problems categories.
This 3rd edition provides an insight into the mathematical crossroads formed by functional analysis (the macroscopic approach), partial differential equations (the mesoscopic approach) and probability (the microscopic approach) via the mathematics needed for the hard parts of Markov processes. It brings these three fields of analysis together, providing a comprehensive study of Markov processes from a broad perspective. The material is carefully and effectively explained, resulting in a surprisingly readable account of the subject. The main focus is on a powerful method for future research in elliptic boundary value problems and Markov processes via semigroups, the Boutet de Monvel calculus. A broad spectrum of readers will easily appreciate the stochastic intuition that this edition conveys. In fact, the book will provide a solid foundation for both researchers and graduate students in pure and applied mathematics interested in functional analysis, partial differential equations, Markov processes and the theory of pseudo-differential operators, a modern version of the classical potential theory.
Boundary Value Problems And Markov Processes
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Author : Kazuaki Taira
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-30
Boundary Value Problems And Markov Processes written by Kazuaki Taira 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 2009-06-30 with Mathematics categories.
This is a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel’ boundary conditions in probability theory. It presents new developments in the theory of singular integrals.
Functional Analytic Techniques For Diffusion Processes
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Author : Kazuaki Taira
language : en
Publisher: Springer Nature
Release Date : 2022-05-28
Functional Analytic Techniques For Diffusion Processes written by Kazuaki Taira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-28 with Mathematics categories.
This book is an easy-to-read reference providing a link between functional analysis and diffusion processes. More precisely, the book takes readers to a mathematical crossroads of functional analysis (macroscopic approach), partial differential equations (mesoscopic approach), and probability (microscopic approach) via the mathematics needed for the hard parts of diffusion processes. This work brings these three fields of analysis together and provides a profound stochastic insight (microscopic approach) into the study of elliptic boundary value problems. The author does a massive study of diffusion processes from a broad perspective and explains mathematical matters in a more easily readable way than one usually would find. The book is amply illustrated; 14 tables and 141 figures are provided with appropriate captions in such a fashion that readers can easily understand powerful techniques of functional analysis for the study of diffusion processes in probability. The scope of the author’s work has been and continues to be powerful methods of functional analysis for future research of elliptic boundary value problems and Markov processes via semigroups. A broad spectrum of readers can appreciate easily and effectively the stochastic intuition that this book conveys. Furthermore, the book will serve as a sound basis both for researchers and for graduate students in pure and applied mathematics who are interested in a modern version of the classical potential theory and Markov processes. For advanced undergraduates working in functional analysis, partial differential equations, and probability, it provides an effective opening to these three interrelated fields of analysis. Beginning graduate students and mathematicians in the field looking for a coherent overview will find the book to be a helpful beginning. This work will be a major influence in a very broad field of study for a long time.
A Short Course On Operator Semigroups
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Author : Klaus-Jochen Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-06
A Short Course On Operator Semigroups written by Klaus-Jochen Engel 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 2006-06-06 with Mathematics categories.
The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. The book is intended for students and researchers who want to become acquainted with the concept of semigroups.
Elliptic Boundary Value Problems
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Author : Kazuaki Taira
language : en
Publisher:
Release Date : 1991
Elliptic Boundary Value Problems written by Kazuaki Taira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Boundary value problems categories.
An Introduction To Continuous Time Stochastic Processes
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Author : Vincenzo Capasso
language : en
Publisher: Springer Nature
Release Date : 2021-06-18
An Introduction To Continuous Time Stochastic Processes written by Vincenzo Capasso and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Mathematics categories.
This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across different fields. Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations. An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularly the applications explored in the second half of the book.
Markov Processes Semigroups And Generators
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Author : Vassili N. Kolokoltsov
language : en
Publisher: Walter de Gruyter
Release Date : 2011-03-29
Markov Processes Semigroups And Generators written by Vassili N. Kolokoltsov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-29 with Mathematics categories.
Markov processes represent a universal model for a large variety of real life random evolutions. The wide flow of new ideas, tools, methods and applications constantly pours into the ever-growing stream of research on Markov processes that rapidly spreads over new fields of natural and social sciences, creating new streamlined logical paths to its turbulent boundary. Even if a given process is not Markov, it can be often inserted into a larger Markov one (Markovianization procedure) by including the key historic parameters into the state space. This monograph gives a concise, but systematic and self-contained, exposition of the essentials of Markov processes, together with recent achievements, working from the "physical picture" - a formal pre-generator, and stressing the interplay between probabilistic (stochastic differential equations) and analytic (semigroups) tools. The book will be useful to students and researchers. Part I can be used for a one-semester course on Brownian motion, Lévy and Markov processes, or on probabilistic methods for PDE. Part II mainly contains the author's research on Markov processes. From the contents: Tools from Probability and Analysis Brownian motion Markov processes and martingales SDE, ψDE and martingale problems Processes in Euclidean spaces Processes in domains with a boundary Heat kernels for stable-like processes Continuous-time random walks and fractional dynamics Complex chains and Feynman integral
Stochastic Calculus Of Variations
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Author : Yasushi Ishikawa
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-03-07
Stochastic Calculus Of Variations written by Yasushi Ishikawa and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-07 with Mathematics categories.
This monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book "processes with jumps" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) "with jumps". The book also contains some applications of the stochastic calculus for processes with jumps to the control theory and mathematical finance. Namely, asymptotic expansions functionals related with financial assets of jump-diffusion are provided based on the theory of asymptotic expansion on the Wiener–Poisson space. Solving the Hamilton–Jacobi–Bellman (HJB) equation of integro-differential type is related with solving the classical Merton problem and the Ramsey theory. The field of jump processes is nowadays quite wide-ranging, from the Lévy processes to SDEs with jumps. Recent developments in stochastic analysis have enabled us to express various results in a compact form. Up to now, these topics were rarely discussed in a monograph. Contents: Preface Preface to the second edition Introduction Lévy processes and Itô calculus Perturbations and properties of the probability law Analysis of Wiener–Poisson functionals Applications Appendix Bibliography List of symbols Index