Boundary Value Problems and Markov Processes

Boundary Value Problems and Markov Processes
Title Boundary Value Problems and Markov Processes PDF eBook
Author Kazuaki Taira
Publisher Springer Science & Business Media
Pages 196
Release 2009-06-30
Genre Mathematics
ISBN 3642016766

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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.

Semigroups, Boundary Value Problems and Markov Processes

Semigroups, Boundary Value Problems and Markov Processes
Title Semigroups, Boundary Value Problems and Markov Processes PDF eBook
Author Kazuaki Taira
Publisher Springer
Pages 724
Release 2014-08-07
Genre Mathematics
ISBN 3662436965

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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.

Markov Processes, Semigroups, and Generators

Markov Processes, Semigroups, and Generators
Title Markov Processes, Semigroups, and Generators PDF eBook
Author Vassili N. Kolokoltsov
Publisher Walter de Gruyter
Pages 449
Release 2011
Genre Mathematics
ISBN 3110250101

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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

Real Analysis Methods for Markov Processes

Real Analysis Methods for Markov Processes
Title Real Analysis Methods for Markov Processes PDF eBook
Author Kazuaki Taira
Publisher Springer Nature
Pages 749
Release
Genre
ISBN 9819736595

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Markov Processes and Related Problems of Analysis

Markov Processes and Related Problems of Analysis
Title Markov Processes and Related Problems of Analysis PDF eBook
Author Evgeniĭ Borisovich Dynkin
Publisher Cambridge University Press
Pages 325
Release 1982-09-23
Genre Mathematics
ISBN 0521285127

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The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics. Professor Dynkin has made many profound contributions to the subject and in this volume are collected several of his most important expository and survey articles. The content of these articles has not been covered in any monograph as yet. This account is accessible to graduate students in mathematics and operations research and will be welcomed by all those interested in stochastic processes and their applications.

Optimal Stopping and Free-Boundary Problems

Optimal Stopping and Free-Boundary Problems
Title Optimal Stopping and Free-Boundary Problems PDF eBook
Author Goran Peskir
Publisher Springer Science & Business Media
Pages 515
Release 2006-11-10
Genre Mathematics
ISBN 3764373903

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This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.

Monte Carlo Methods

Monte Carlo Methods
Title Monte Carlo Methods PDF eBook
Author Karl K. Sabelfeld
Publisher Springer
Pages 0
Release 2011-12-13
Genre Science
ISBN 9783642759796

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This book deals with Random Walk Methods for solving multidimensional boundary value problems. Monte Carlo algorithms are constructed for three classes of problems: (1) potential theory, (2) elasticity, and (3) diffusion. Some of the advantages of our new methods as compared to conventional numerical methods are that they cater for stochasticities in the boundary value problems and complicated shapes of the boundaries.