On The Existence Of Feller Semigroups With Boundary Conditions

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On the Existence of Feller Semigroups with Boundary Conditions

Author : Kazuaki Taira
Publisher : American Mathematical Soc.
ISBN 13 : 0821825356
Total Pages : 81 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On the Existence of Feller Semigroups with Boundary Conditions by : Kazuaki Taira

Download or read book On the Existence of Feller Semigroups with Boundary Conditions written by Kazuaki Taira and published by American Mathematical Soc.. This book was released on 1992 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups with Ventcel' (Wentzell) boundary conditions. This paper considers the non-transversal case and solves from the viewpoint of functional analysis the problem of construction of Feller semigroups for elliptic Waldenfels operators. Intuitively, our result may be stated as follows: One can construct a Feller semigroup corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it "dies" at which time it reaches the set where the absorption phenomenon occurs.

Semigroups, Boundary Value Problems and Markov Processes

Author : Kazuaki Taira
Publisher : Springer
ISBN 13 : 3662436965
Total Pages : 724 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Semigroups, Boundary Value Problems and Markov Processes by : Kazuaki Taira

Download or read book Semigroups, Boundary Value Problems and Markov Processes written by Kazuaki Taira and published by Springer. This book was released on 2014-08-07 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Kazuaki Taira
Publisher : Springer Nature
ISBN 13 : 3030487881
Total Pages : 502 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Boundary Value Problems and Markov Processes by : Kazuaki Taira

Download or read book Boundary Value Problems and Markov Processes written by Kazuaki Taira and published by Springer Nature. This book was released on 2020-07-01 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Functional Analytic Techniques for Diffusion Processes

Author : Kazuaki Taira
Publisher : Springer Nature
ISBN 13 : 9811910995
Total Pages : 792 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Functional Analytic Techniques for Diffusion Processes by : Kazuaki Taira

Download or read book Functional Analytic Techniques for Diffusion Processes written by Kazuaki Taira and published by Springer Nature. This book was released on 2022-05-28 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Semigroups of Operators: Theory and Applications

Author : A.V. Balakrishnan
Publisher : Birkhäuser
ISBN 13 : 3034884176
Total Pages : 376 pages
Book Rating : 4.0/5 (348 download)

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

Download or read book Semigroups of Operators: Theory and Applications written by A.V. Balakrishnan and published by Birkhäuser. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Markov Operators, Positive Semigroups and Approximation Processes

Author : Francesco Altomare
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110386410
Total Pages : 325 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Markov Operators, Positive Semigroups and Approximation Processes by : Francesco Altomare

Download or read book Markov Operators, Positive Semigroups and Approximation Processes written by Francesco Altomare and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-12-18 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Markov Processes, Semigroups, and Generators

Author : Vassili N. Kolokoltsov
Publisher : Walter de Gruyter
ISBN 13 : 3110250101
Total Pages : 449 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Markov Processes, Semigroups, and Generators by : Vassili N. Kolokoltsov

Download or read book Markov Processes, Semigroups, and Generators written by Vassili N. Kolokoltsov and published by Walter de Gruyter. This book was released on 2011 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Computation and Applied Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 100 pages
Book Rating : 4./5 ( download)

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Book Synopsis Computation and Applied Mathematics by :

Download or read book Computation and Applied Mathematics written by and published by . This book was released on 1997 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Interaction Between Functional Analysis, Harmonic Analysis, and Probability

Author : Nigel Kalton
Publisher : CRC Press
ISBN 13 : 9780824796112
Total Pages : 496 pages
Book Rating : 4.7/5 (961 download)

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Book Synopsis Interaction Between Functional Analysis, Harmonic Analysis, and Probability by : Nigel Kalton

Download or read book Interaction Between Functional Analysis, Harmonic Analysis, and Probability written by Nigel Kalton and published by CRC Press. This book was released on 1995-10-12 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Trends In Probability And Related Analysis - Proceedings Of Sap'98

Author : N Kono
Publisher : World Scientific
ISBN 13 : 9814543527
Total Pages : 322 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Trends In Probability And Related Analysis - Proceedings Of Sap'98 by : N Kono

Download or read book Trends In Probability And Related Analysis - Proceedings Of Sap'98 written by N Kono and published by World Scientific. This book was released on 1999-10-19 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Boundary Value Problems and Markov Processes

Author : Kazuaki Taira
Publisher : Springer
ISBN 13 : 3642016774
Total Pages : 196 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Boundary Value Problems and Markov Processes by : Kazuaki Taira

Download or read book Boundary Value Problems and Markov Processes written by Kazuaki Taira and published by Springer. This book was released on 2009-06-17 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lévy Processes

Author : Ole E Barndorff-Nielsen
Publisher : Springer Science & Business Media
ISBN 13 : 1461201977
Total Pages : 414 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Lévy Processes by : Ole E Barndorff-Nielsen

Download or read book Lévy Processes written by Ole E Barndorff-Nielsen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Stochastic Differential Equations with Reflection

Author : Andrey Pilipenko
Publisher : Universitätsverlag Potsdam
ISBN 13 : 3869562978
Total Pages : 90 pages
Book Rating : 4.8/5 (695 download)

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Book Synopsis An Introduction to Stochastic Differential Equations with Reflection by : Andrey Pilipenko

Download or read book An Introduction to Stochastic Differential Equations with Reflection written by Andrey Pilipenko and published by Universitätsverlag Potsdam. This book was released on 2014 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computation and Applied Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 100 pages
Book Rating : 4./5 ( download)

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Book Synopsis Computation and Applied Mathematics by :

Download or read book Computation and Applied Mathematics written by and published by . This book was released on 1997 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computation and Applied Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 100 pages
Book Rating : 4./5 ( download)

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Book Synopsis Computation and Applied Mathematics by :

Download or read book Computation and Applied Mathematics written by and published by . This book was released on 1997 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elliptic Functional Differential Equations and Applications

Author : Alexander L. Skubachevskii
Publisher : Birkhäuser
ISBN 13 : 3034890338
Total Pages : 298 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Elliptic Functional Differential Equations and Applications by : Alexander L. Skubachevskii

Download or read book Elliptic Functional Differential Equations and Applications written by Alexander L. Skubachevskii and published by Birkhäuser. This book was released on 2012-12-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Markov Processes and Kinetic Equations

Author : Vassili N. Kolokoltsov
Publisher : Cambridge University Press
ISBN 13 : 1139489739
Total Pages : 394 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Nonlinear Markov Processes and Kinetic Equations by : Vassili N. Kolokoltsov

Download or read book Nonlinear Markov Processes and Kinetic Equations written by Vassili N. Kolokoltsov and published by Cambridge University Press. This book was released on 2010-07-15 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.