Semigroups, Boundary Value Problems and Markov Processes (Springer Monographs in Mathematics)

A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which 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. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes and Comments where bibliographical references are primarily discussed. Thanks to the kind feedback from many readers, some errors in the first edition have been corrected. In order to keep the book up-to-date, new references have been added to the bibliography. Researchers and graduate students interested in PDEs, functional analysis and probability will find this volume useful.

Dr. Kazuaki TAIRA, born in Tokyo (Japan) on 1 January, 1946, served for many years as a professor of mathematics at the University of Tsukuba (1998-2009). He received his Bachelor of Science degree in 1969 from the University of Tokyo, Japan and his Master of Science degree in 1972 from Tokyo Institute of Technology, Japan, where he served as an assistant from 1972 until 1978. The Doctor of Science degree was awarded to him on 21 June, 1976 by the University of Tokyo and on 13 June, 1978 the Doctorat d'Etat degree was given to him by Universite de Paris-Sud, France. He had been studying there on the French government scholarship from 1976 until 1978.
Dr. TAIRA was also a member of the Institute for Advanced Study (Princeton), U. S. A. (1980-1981), and was an associate professor at the University of Tsukuba (1981-1995), and a professor at Hiroshima University, Japan (1995-1998). In 1998, he accepted an invitation from the University of Tsukuba to teach there again as a professor. Since 2009, he is a part-time professor at Waseda University in Tokyo.
His current research interests are in the study of three interrelated subjects in analysis: semi groups, elliptic boundary value problems and Markov processes.