Probability Theory, Statistics, Mathematics - Group Theory, Mathematical Equations - Differential

Semigroups, Boundary Value Problems and Markov Processes

Name: Semigroups, Boundary Value Problems and Markov Processes
Author: Taira, Kazuaki
ISBN: 9783642073717

by Taira, Kazuaki

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Overview

The purpose of this book is to provide a careful and accessible account of the subject along modern lines, as well as to discuss problems of current interest in the field. More precisely, this book is devoted to the functional-analytic approach to a class of degenerate boundary value problems for second-order elliptic integro-differential operators which includes as particular cases the Dirichlet and Robin problems. This class of boundary value problems provides a new example of analytic semigroups. As an application, we construct a strong Markov process corresponding to a diffusion phenomenon such that a Markovian particle moves both by jumps and continuously in the state space until it dies at the time when it reaches the set where the particle is definitely absorbed.

About the Author, Taira, Kazuaki

Kazuaki TAIRA is Professor of Mathematics at the University of Tsukuba, Japan, where he has taught since 1998. He received his Bachelor of Science (1969) degree from the University of Tokyo, Japan, and his Master of Science (1972) degree from Tokyo Institute of Technology, Japan, where he served as an Assistant between 1972-1978. He holds the Doctor of Science (1976) degree from the University of Tokyo, and the Doctorat d'Etat (1978) degree from Université de Paris-Sud, France, where he received a French Government Scholarship in 1976-1978. Dr. Taira was also a member of the Institute for Advanced Study, U. S. A., in 1980-1981. He was Associate Professor of the University of Tsukuba between 1981-1995, and Professor of Hiroshima University, Japan, between 1995-1998.

His current research interests are in the study of three interrelated subjects in analysis: semigroups, elliptic boundary value problems and Markov processes.