Boundary Value Problems and Markov Processes
Functional Analysis Methods for Markov Processes
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Beschreibung
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.
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.
Introduces readers to a mathematical crossroads in analysis: semigroups, elliptic boundary value problems and Markov processes Presents principal ideas explicitly so that a broad spectrum of readers can easily understand the relationship between partial differential equations and probability in analysis Is amply illustrated with 136 figures and 15 tables Describes a powerful new method for future research, the Boutet de Monvel calculus
Autor*in
Kazuaki Taira
Themen in »Boundary Value Problems and Markov Processes«
Analytic Semigroup Boundary Value Problem Boutet de Monvel Calculus Elliptic Boundary Value Problem Feller Semigroup Markov Process Pseudo-differential Operator Semilinear Parabolic Equation
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“By reading this book, a broad spectrum of readers will be able to understand and appreciate the mathematical crossroads of functional analysis, boundary value problems, and probability theory as developed in the more advanced books … . this book provides a compendium for a large variety of facts from functional analysis, pseudo-differential operators, and Markov processes. Indeed, it gives detailed coverage of important examples and applications in this area.” (J. A. van Casteren, Mathematical Reviews, October, 2022)
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