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Boundary Value Problems and Markov Processes: Functional Analysis Methods for Markov Processes

Boundary Value Problems and Markov Processes: Functional Analysis Methods for Markov Processes

Autorzy
Wydawnictwo Springer Nature Switzerland AG
Data wydania 02/07/2020
Wydanie Trzecie
Liczba stron 502
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
ISBN 9783030487874
Kategorie Rachunek matematyczny i analizy matematyczne, Analizy funkcjonalne i przekształcenia, Prawdopodobieństwo i statystyka
Zastępuje 9783642016769
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Opis książki

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.

Boundary Value Problems and Markov Processes: Functional Analysis Methods for Markov Processes

Spis treści

- Preface to the Third Edition. - Preface to the Second Edition. - Introduction and Main Results. - Part I Analytic and Feller Semigroups and Markov Processes. - Analytic Semigroups. - Markov Processes and Feller Semigroups. - Part II Pseudo-Differential Operators and Elliptic Boundary Value Problems. - Lp Theory of Pseudo-Differential Operators. - Boutet de Monvel Calculus. - Lp Theory of Elliptic Boundary Value Problems. - Part III Analytic Semigroups in Lp Sobolev Spaces. - Proof of Theorem 1.2. - A Priori Estimates. - Proof of Theorem 1.4. - Part IV Waldenfels Operators, Boundary Operators and Maximum Principles. - Elliptic Waldenfels Operators and Maximum Principles. - Boundary Operators and Boundary Maximum Principles. - Part V Feller Semigroups for Elliptic Waldenfels Operators. - Proof of Theorem 1.5 - Part (i). - Proofs of Theorem 1.5, Part (ii) and Theorem 1.6. - Proofs of Theorems 1.8, 1.9, 1.10 and 1.11. - Path Functions of Markov Processes via Semigroup Theory. - Part VI Concluding Remarks. - The State-of-the-Art of Generation Theorems for Feller Semigroups.

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