Overview
- Guides readers to a mathematical crossroads in analysis
- Provides powerful techniques of functional analysis (macroscopic approach) for the study of diffusion processes
- Furnishes a profound stochastic insight into the study of elliptic boundary value problems
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (14 chapters)
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Foundations of Modern Analysis
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Elements of Partial Differential Equations
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Maximum Principles and Elliptic Boundary Value Problems
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L2 Theory of Elliptic Boundary Value Problems
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Markov Processes, Feller Semigroups and Boundary Value Problems
Keywords
About this book
The author does a massive study of diffusion processes from a broad perspective and explains mathematical matters in a more easily readable way than one usually would find. The book is amply illustrated; 14 tables and 141 figures are provided with appropriate captions in such a fashion that readers can easily understand powerful techniques of functional analysis for the study of diffusion processes in probability.
The scope of the author’s work has been and continues to be powerful methods of functional analysis for future research of elliptic boundary value problems and Markov processes via semigroups. A broad spectrum of readers can appreciate easily and effectively the stochastic intuition that this book conveys. Furthermore, the book will serve as a sound basis both for researchers and for graduate students in pure and applied mathematics who are interested in a modern version of the classical potential theory and Markov processes.
For advanced undergraduates working in functional analysis, partial differential equations, and probability, it provides an effective opening to these three interrelated fields of analysis. Beginning graduate students and mathematicians in the field looking for a coherent overview will find the book to be a helpful beginning.
This work will be a major influence in a very broad field of study for a long time.
Authors and Affiliations
Bibliographic Information
Book Title: Functional Analytic Techniques for Diffusion Processes
Authors: Kazuaki Taira
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-981-19-1099-9
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022
Hardcover ISBN: 978-981-19-1098-2Published: 30 May 2022
Softcover ISBN: 978-981-19-1101-9Published: 31 May 2023
eBook ISBN: 978-981-19-1099-9Published: 28 May 2022
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XXII, 782
Number of Illustrations: 147 b/w illustrations
Topics: Functional Analysis, Probability Theory and Stochastic Processes