ENGLISH

Boundary Value Problems and Markov Processes

By Kazuaki Taira (auth.)

Book information

Publisher
Springer Berlin Heidelberg
Year
1991
ISBN
9780387549965, 038754996X, 354054996X
DOI
10.1007/BFb0092029
LCC
QA3 .L28 no. 1499, 1991,QA379 .L28 no. 1499,
Open Library ID
OL1288419M
Language
english
Format
DJVU
Filesize
716 kB (733004 bytes)
Series
Lecture Notes in Mathematics 1499
Pages
146\146
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11
Analysis; Probability Theory and Stochastic Proces

Description

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.

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