On The Existence Of Feller Semigroups With Boundary Conditions

Author : Kazuaki Taira
Publisher : American Mathematical Soc.
Page : 65 pages
File Size : 48,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825358

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On the Existence of Feller Semigroups with Boundary Conditions by Kazuaki Taira Pdf

This monograph provides a careful and accessible exposition of functional analytic methods in stochastic analysis. The author focuses on the relationship among three subjects in analysis: Markov processes, Feller semigroups, and elliptic boundary value problems. The approach here is distinguished by the author's extensive use of the theory of partial differential equations. Filling a mathematical gap between textbooks on Markov processes and recent developments in analysis, this work describes a powerful method capable of extensive further development. The book would be suitable as a textbook in a one-year, advanced graduate course on functional analysis and partial differential equations, with emphasis on their strong interrelations with probability theory.

Author : Kazuaki Taira
Publisher : Springer
Page : 724 pages
File Size : 47,6 Mb
Release : 2014-08-07
Category : Mathematics
ISBN : 9783662436967

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Semigroups, Boundary Value Problems and Markov Processes by Kazuaki Taira Pdf

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.

Author : Kazuaki Taira
Publisher : Springer Nature
Page : 502 pages
File Size : 50,6 Mb
Release : 2020-07-01
Category : Mathematics
ISBN : 9783030487881

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Boundary Value Problems and Markov Processes by Kazuaki Taira Pdf

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.

Author : Kazuaki Taira
Publisher : Springer Nature
Page : 792 pages
File Size : 41,6 Mb
Release : 2022-05-28
Category : Mathematics
ISBN : 9789811910999

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Functional Analytic Techniques for Diffusion Processes by Kazuaki Taira Pdf

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.

Author : Francesco Altomare,Mirella Cappelletti,Vita Leonessa,Ioan Rasa
Publisher : Walter de Gruyter GmbH & Co KG
Page : 325 pages
File Size : 55,9 Mb
Release : 2015-12-18
Category : Mathematics
ISBN : 9783110386417

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Markov Operators, Positive Semigroups and Approximation Processes by Francesco Altomare,Mirella Cappelletti,Vita Leonessa,Ioan Rasa Pdf

In recent years several investigations have been devoted to the study of large classes of (mainly degenerate) initial-boundary value evolution problems in connection with the possibility to obtain a constructive approximation of the associated positive C_0-semigroups. In this research monograph we present the main lines of a theory which finds its root in the above-mentioned research field.

Author : A.V. Balakrishnan
Publisher : Birkhäuser
Page : 376 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034884174

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Semigroups of Operators: Theory and Applications by A.V. Balakrishnan Pdf

These Proceedings comprise the bulk of the papers presented at the Inter national Conference on Semigroups of Opemtors: Theory and Contro~ held 14-18 December 1998, Newport Beach, California, U.S.A. The intent of the Conference was to highlight recent advances in the the ory of Semigroups of Operators which provides the abstract framework for the time-domain solutions of time-invariant boundary-value/initial-value problems of partial differential equations. There is of course a firewall between the ab stract theory and the applications and one of the Conference aims was to bring together both in the hope that it may be of value to both communities. In these days when all scientific activity is judged by its value on "dot com" it is not surprising that mathematical analysis that holds no promise of an immediate commercial product-line, or even a software tool-box, is not high in research priority. We are particularly pleased therefore that the National Science Foundation provided generous financial support without which this Conference would have been impossible to organize. Our special thanks to Dr. Kishan Baheti, Program Manager.

Author : Vassili N. Kolokoltsov
Publisher : Walter de Gruyter
Page : 449 pages
File Size : 51,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9783110250107

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Markov Processes, Semigroups, and Generators by Vassili N. Kolokoltsov Pdf

This work offers a highly useful, well developed reference on Markov processes, the universal model for random processes and evolutions. The wide range of applications, in exact sciences as well as in other areas like social studies, require a volume that offers a refresher on fundamentals before conveying the Markov processes and examples for

Author : Nigel Kalton,Elias Saab,Stephen Montgomery-Smith
Publisher : CRC Press
Page : 496 pages
File Size : 46,9 Mb
Release : 1995-10-12
Category : Mathematics
ISBN : 082479611X

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Interaction Between Functional Analysis, Harmonic Analysis, and Probability by Nigel Kalton,Elias Saab,Stephen Montgomery-Smith Pdf

Based on a conference on the interaction between functional analysis, harmonic analysis and probability theory, this work offers discussions of each distinct field, and integrates points common to each. It examines developments in Fourier analysis, interpolation theory, Banach space theory, probability, probability in Banach spaces, and more.

Author : N Kono,Narn-rueih Shieh
Publisher : World Scientific
Page : 322 pages
File Size : 55,8 Mb
Release : 1999-10-19
Category : Electronic
ISBN : 9789814543521

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Trends In Probability And Related Analysis - Proceedings Of Sap'98 by N Kono,Narn-rueih Shieh Pdf

This proceedings volume reflects the current interest in and future direction of probability theory and related theory of analysis and statistics. It contains 2 survey papers and 21 contributed papers.

Author : Kazuaki Taira
Publisher : Springer
Page : 192 pages
File Size : 43,7 Mb
Release : 2009-06-17
Category : Mathematics
ISBN : 9783642016776

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Boundary Value Problems and Markov Processes by Kazuaki Taira Pdf

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.

Author : Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201977

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Lévy Processes by Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick Pdf

A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.

Author : Klaus-Jochen Engel,Rainer Nagel
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 45,9 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387226422

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One-Parameter Semigroups for Linear Evolution Equations by Klaus-Jochen Engel,Rainer Nagel Pdf

This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on philosophical motivation and the historical background.

Author : Andrey Pilipenko
Publisher : Universitätsverlag Potsdam
Page : 90 pages
File Size : 52,8 Mb
Release : 2014
Category : Electronic
ISBN : 9783869562971

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An Introduction to Stochastic Differential Equations with Reflection by Andrey Pilipenko Pdf

Author : Alexander L. Skubachevskii
Publisher : Birkhäuser
Page : 298 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890335

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Elliptic Functional Differential Equations and Applications by Alexander L. Skubachevskii Pdf

Boundary value problems for elliptic differential-difference equations have some astonishing properties. For example, unlike elliptic differential equations, the smoothness of the generalized solutions can be broken in a bounded domain and is preserved only in some subdomains. The symbol of a self-adjoint semibounded functional differential operator can change its sign. The purpose of this book is to present for the first time general results concerning solvability and spectrum of these problems, a priori estimates and smoothness of solutions. The approach is based on the properties of elliptic operators and difference operators in Sobolev spaces. The most important features distinguishing this work are applications to different fields of science. The methods in this book are used to obtain new results regarding the solvability of nonlocal elliptic boundary value problems and the existence of Feller semigroups for multidimensional diffusion processes. Moreover, applications to control theory and aircraft and rocket technology are given. The theory is illustrated with numerous figures and examples. The book is addresssed to graduate students and researchers in partial differential equations and functional differential equations. It will also be of use to engineers in control theory and elasticity theory.

Author : Vassili N. Kolokoltsov
Publisher : Cambridge University Press
Page : 394 pages
File Size : 52,7 Mb
Release : 2010-07-15
Category : Mathematics
ISBN : 9781139489737

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Nonlinear Markov Processes and Kinetic Equations by Vassili N. Kolokoltsov Pdf

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.