Lecture Notes in Mathematics

Boundary Value Problems and Markov Processes

Authors: Taira, Kazuaki

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About this book

Focussing on the interrelations of the subjects of Markov processes, analytic semigroups and elliptic boundary value problems, this monograph provides a careful and accessible exposition of functional methods in stochastic analysis. The author studies a class of boundary value problems for second-order elliptic differential operators which includes as particular cases the Dirichlet and Neumann problems, and proves that this class of boundary value problems provides a new example of analytic semigroups both in the Lp topology and in the topology of uniform convergence. As an application, one can construct analytic semigroups corresponding to the diffusion phenomenon of a Markovian particle moving continuously in the state space until it "dies", at which time it reaches the set where the absorption phenomenon occurs. A class of initial-boundary value problems for semilinear parabolic differential equations is also considered. This monograph will appeal to both advanced students and researchers as an introduction to the three interrelated subjects in analysis, providing powerful methods for continuing research.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $74.99
price for USA in USD
  • ISBN 978-3-540-46635-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Boundary Value Problems and Markov Processes
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1499
Copyright
1991
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-46635-2
DOI
10.1007/BFb0092029
Series ISSN
0075-8434
Edition Number
1
Number of Pages
IX, 132
Topics