Download or read book Boundary Value Problems and Markov Processes written by Kazuaki Taira and published by Springer Science & Business Media. This book was released on 2009-06-30 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.
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.
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.
Download or read book Analytic Semigroups and Semilinear Initial Boundary Value Problems written by Kazuaki Taira and published by Cambridge University Press. This book was released on 2016-04-28 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition explores the relationship between elliptic and parabolic initial boundary value problems, for undergraduate and graduate students.
Download or read book Elliptic Boundary Value Problems written by Kazuaki Taira and published by . This book was released on 1991 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
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 1992-09-02 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph gives a detailed account of a theory which is mainly concerned with certain classes of degenerate differential operators, Markov semigroups and approximation processes. These mathematical objects are generated by arbitrary Markov operators acting on spaces of continuous functions defined on compact convex sets; the study of the interrelations between them constitutes one of the distinguishing features of the book. Among other things, this theory provides useful tools for studying large classes of initial-boundary value evolution problems, the main aim being to obtain a constructive approximation to the associated positive C0-semigroups by means of iterates of suitable positive approximating operators. As a consequence, a qualitative analysis of the solutions to the evolution problems can be efficiently developed. The book is mainly addressed to research mathematicians interested in modern approximation theory by positive linear operators and/or in the theory of positive C0-semigroups of operators and evolution equations. It could also serve as a textbook for a graduate level course.
Download or read book Real Analysis Methods for Markov Processes written by Kazuaki Taira and published by Springer Nature. This book was released on with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Real Analysis Methods for Markov Processes written by Kazuaki Taira and published by Springer. This book was released on 2024-08-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to real analysis methods for the problem of constructing Markov processes with boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called the Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel (Wentzell) boundary condition, on the boundary of the domain. Most likely, a Markovian particle moves both by continuous paths and by jumps in the state space and obeys the Ventcel boundary condition, which consists of six terms corresponding to diffusion along the boundary, an absorption phenomenon, a reflection phenomenon, a sticking (or viscosity) phenomenon, and a jump phenomenon on the boundary and an inward jump phenomenon from the boundary. More precisely, we study a class of first-order Ventcel boundary value problems for second-order elliptic Waldenfels integro-differential operators. By using the Calderón–Zygmund theory of singular integrals, we prove the existence and uniqueness of theorems in the framework of the Sobolev and Besov spaces, which extend earlier theorems due to Bony–Courrège–Priouret to the vanishing mean oscillation (VMO) case. Our proof is based on various maximum principles for second-order elliptic differential operators with discontinuous coefficients in the framework of Sobolev spaces. My approach is distinguished by the extensive use of the ideas and techniques characteristic of recent developments in the theory of singular integral operators due to Calderón and Zygmund. Moreover, we make use of an Lp variant of an estimate for the Green operator of the Neumann problem introduced in the study of Feller semigroups by me. The present book is amply illustrated; 119 figures and 12 tables are provided in such a fashion that a broad spectrum of readers understand our problem and main results.
Download or read book Analytical Methods for Markov Semigroups written by Luca Lorenzi and published by CRC Press. This book was released on 2006-07-28 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first time in book form, Analytical Methods for Markov Semigroups provides a comprehensive analysis on Markov semigroups both in spaces of bounded and continuous functions as well as in Lp spaces relevant to the invariant measure of the semigroup. Exploring specific techniques and results, the book collects and updates the literature associated with Markov semigroups. Divided into four parts, the book begins with the general properties of the semigroup in spaces of continuous functions: the existence of solutions to the elliptic and to the parabolic equation, uniqueness properties and counterexamples to uniqueness, and the definition and properties of the weak generator. It also examines properties of the Markov process and the connection with the uniqueness of the solutions. In the second part, the authors consider the replacement of RN with an open and unbounded domain of RN. They also discuss homogeneous Dirichlet and Neumann boundary conditions associated with the operator A. The final chapters analyze degenerate elliptic operators A and offer solutions to the problem. Using analytical methods, this book presents past and present results of Markov semigroups, making it suitable for applications in science, engineering, and economics.
Download or read book Generators of Markov Chains written by Adam Bobrowski and published by Cambridge University Press. This book was released on 2020-11-26 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear explanation of what an explosive Markov chain does after it passes through all available states in finite time.
Download or read book Diffusion Processes and Partial Differential Equations written by Kazuaki Taira and published by . This book was released on 1988 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a careful and accessible exposition of functional analytic methods in stochastic analysis. It focuses on the relationship between Markov processes and elliptic boundary value problems and explores several recent developments in the theory of partial differential equations which have made further progress in the study of Markov processes possible. This book will have great appeal to both advanced students and researchers as an introduction to three interrelated subjects in analysis (Markov processes, semigroups, and elliptic boundary value problems), providing powerful methods for future research.
Download or read book Hyperfinite Dirichlet Forms and Stochastic Processes written by Sergio Albeverio and published by Springer Science & Business Media. This book was released on 2011-05-27 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph treats the theory of Dirichlet forms from a comprehensive point of view, using "nonstandard analysis." Thus, it is close in spirit to the discrete classical formulation of Dirichlet space theory by Beurling and Deny (1958). The discrete infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same methods. This setting has the advantage of being independent of special topological properties of the state space and in this sense is a natural one, valid for both finite- and infinite-dimensional spaces. The present monograph provides a thorough treatment of the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes, and summarizes in an epilogue the model-theoretic genericity of hyperfinite stochastic processes theory.
Download or read book Symmetric Markov Processes Time Change and Boundary Theory LMS 35 written by Zhen-Qing Chen and published by Princeton University Press. This book was released on 2012 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes. This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.
Download or read book A Short Course on Operator Semigroups written by Klaus-Jochen Engel and published by Springer Science & Business Media. This book was released on 2006-10-14 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. It contains the fundamental results of the theory such as the Hille-Yoshida generation theorem, the bounded perturbation theorem, and the Trotter-Kato approximation theorem. It also treats the spectral theory of semigroups and its consequences for the qualitative behavior. The book is intended for students and researchers who want to become acquainted with the concept of semigroups in order to work with it in fields like partial and functional differential equations. Exercises are provided at the end of the chapters.
