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Boundary Value Problems and Markov Processes

2009-06-30 Mathematics
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Release : 2009-06-30
Genre : Mathematics
Kind : eBook
Book Rating : 766/5 ( reviews)

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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. This book was released on 2009-06-30. 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.

Boundary Value Problems and Markov Processes

2020-07-01 Mathematics
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Release : 2020-07-01
Genre : Mathematics
Kind : eBook
Book Rating : 881/5 ( reviews)

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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. This book was released on 2020-07-01. 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.

Semigroups, Boundary Value Problems and Markov Processes

2014-08-07 Mathematics
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Release : 2014-08-07
Genre : Mathematics
Kind : eBook
Book Rating : 965/5 ( reviews)

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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. This book was released on 2014-08-07. 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.

Markov Processes and Differential Equations

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 911/5 ( reviews)

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Book Synopsis Markov Processes and Differential Equations by : Mark I. Freidlin

Download or read book Markov Processes and Differential Equations written by Mark I. Freidlin. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations. Due to the close connection between the second order differential operators with a non-negative characteristic form on the one hand and Markov processes on the other, many problems in PDE's can be reformulated as problems for corresponding stochastic processes and vice versa. In the present book four classes of problems are considered: - the Dirichlet problem with a small parameter in higher derivatives for differential equations and systems - the averaging principle for stochastic processes and PDE's - homogenization in PDE's and in stochastic processes - wave front propagation for semilinear differential equations and systems. From the probabilistic point of view, the first two topics concern random perturbations of dynamical systems. The third topic, homog- enization, is a natural problem for stochastic processes as well as for PDE's. Wave fronts in semilinear PDE's are interesting examples of pattern formation in reaction-diffusion equations. The text presents new results in probability theory and their applica- tion to the above problems. Various examples help the reader to understand the effects. Prerequisites are knowledge in probability theory and in partial differential equations.

Elliptic Boundary Value Problems

1991 Boundary value problems
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Release : 1991
Genre : Boundary value problems
Kind : eBook
Book Rating : 965/5 ( reviews)

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Book Synopsis Elliptic Boundary Value Problems by : Kazuaki Taira

Download or read book Elliptic Boundary Value Problems written by Kazuaki Taira. This book was released on 1991. Available in PDF, EPUB and Kindle. Book excerpt:

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