Boundary value problems and Markov processes: functional analysis methods for Markov processes
This third 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 surpr…
Read More ↓Title Statements
- Full title :Boundary value problems and Markov processes : functional analysis methods for Markov processes / Taira Kazuaki.
Summary
This third 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.
Read More ↓Edition Statements
- Publication Date:©2020
- Edition:Third edition
Publication Statements
- Publisher(s):Springer
- Place of Publication:Cham
- Language:eng
- Publication Date:©2020
The Physical Object
- Description:xvii, 500 pages : : illustrations ; : 24 cm
Edition Identifiers
- ISBN:3030487873, 9783030487874
- oclc:on1152390980
- LC Classification:QA3
Table of Contents
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.
Read More ↓Subjects
Writers
More from this Series
No reviews yet. Be the first to rate this work.
Related Works
more →
Copula-based Markov models for time series: parametric inference and process control
Sun, Li-Hsien
Copula-based Markov models for time series: parametric inference and process control
Sun, Li-Hsien
Boundary value problems and Markov processes: functional analysis methods for Markov …
Taira, Kazuaki
Boundary value problems and Markov processes: functional analysis methods for Markov …
Taira, Kazuaki
Markov processes: characterization and convergence
Rate & Review