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

Taira, Kazuaki

Hardcover

ISBN 10: 3662436957 ISBN 13: 9783662436950

Publisher: Springer, 2014

Synopsis

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.

About this title

About the Author

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.

Review

From the reviews: "This book is devoted to the study of certain uniformly elliptic boundary value problems and associated semigroups. The main results are all laid out in the introduction, so it is always clear where the book is headed. For the probabilist, the book provides a good introduction to modern sophisticated results on analytical problems associated with diffusion processes with possibly additional Levy-type jumps. In some cases, the book may also be a useful reference ." (Jan M. Swart, Jahresberichte der Deutschen Mathematiker Vereinigung, November, 2005) "This book by Kazuaki Taira contains a detailed study of semigroups, elliptical boundary value problems, Markov processes and the relations between these mathematical concepts. The book grew out of a series of lectures and lecture notes; this facilitates its use for teaching at the graduate level. The presentation is detailed and clear . I would recommend the book for graduate students or researchers interested mainly in the analytical aspects of Markov process theory ." (R. Frey, ZAA - Zeitschrift fur Analysis und ihre Anwendungen, Vol. 23 (3), 2004) "In this book the author proposes the study of three interrelated subjects in analysis: semigroups, elliptic boundary value problems and Markov processes. The well chosen material given in an appropriate form and style makes the book very useful for the university students as well as for mathematicians with interests in probability theory, functional analysis and partial differential equations." (Mikhail P. Moklyachuk, Zentralblatt MATH, Vol. 1035, 2004) "The book is devoted to the generation of analytic Feller semigroups by operators corresponding to boundary value problems for second order elliptic differential and integro-differential equations. ... the present book is a valuable contribution to a rich field of mathematics emerging at the interface of functional analysis, partial differential equations, and stochastic processes." (Anatoly N. Kochubei, Ma

From the reviews:

"This book is devoted to the study of certain uniformly elliptic boundary value problems and associated semigroups. The main results are all laid out in the introduction, so it is always clear where the book is headed. For the probabilist, the book provides a good introduction to modern sophisticated results on analytical problems associated with diffusion processes with possibly additional Levy-type jumps. In some cases, the book may also be a useful reference ." (Jan M. Swart, Jahresberichte der Deutschen Mathematiker Vereinigung, November, 2005)

"This book by Kazuaki Taira contains a detailed study of semigroups, elliptical boundary value problems, Markov processes and the relations between these mathematical concepts. The book grew out of a series of lectures and lecture notes; this facilitates its use for teaching at the graduate level. The presentation is detailed and clear . I would recommend the book for graduate students or researchers interested mainly in the analytical aspects of Markov process theory ." (R. Frey, ZAA - Zeitschrift fur Analysis und ihre Anwendungen, Vol. 23 (3), 2004)

"In this book the author proposes the study of three interrelated subjects in analysis: semigroups, elliptic boundary value problems and Markov processes. The well chosen material given in an appropriate form and style makes the book very useful for the university students as well as for mathematicians with interests in probability theory, functional analysis and partial differential equations." (Mikhail P. Moklyachuk, Zentralblatt MATH, Vol. 1035, 2004)

"The book is devoted to the generation of analytic Feller semigroups by operators corresponding to boundary value problems for second order elliptic differential and integro-differential equations. ... the present book is a valuable contribution to a rich field of mathematics emerging at the interface of functional analysis, partial differential equations, and stochastic processes." (

Edition details

• Publisher: Springer
• Publication date: 2014
• ISBN 10: 3662436957
• ISBN 13: 9783662436950
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 735