Boundary Value Problems and Markov Processes - Kazuaki Taira

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Résumé :
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. ...

Biographie:
Dr. Kazuaki Taira was awarded a Doctor of Science degree by the University of Tokyo (1976) and a Doctorat d'?tat degree by Universit? de Paris-Sud (Orsay) (1978), where he had studied on a French government scholarship (1976-1978). He was also a member of the Institute for Advanced Study (Princeton) (1980-1981), an associate professor at the University of Tsukuba (1981-1995), and a professor at Hiroshima University (1995-1998). In 1998, he accepted an offer from the University of Tsukuba to teach there again as a professor. He was also a part-time professor at Waseda University (2009-2017). His current research interests are in three interrelated subjects in analysis: semigroups, elliptic boundary value problems and Markov processes....

Sommaire:
Preface to the Third Edition. - ...