Boundary Value Problems and Markov Processes / by Kazuaki Taira.

Format:

Book

Author/Creator:

Taira, Kazuaki, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1499.

Lecture Notes in Mathematics, 0075-8434 ; 1499

Language:

English

Subjects (All):

Global analysis (Mathematics).

Distribution (Probability theory).

Analysis.

Probability Theory and Stochastic Processes.

Local Subjects:

Analysis.

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (IX, 132 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991.

System Details:

text file PDF

Summary:

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.

Contents:

and results

Semigroup theory

L p theory of pseudo-differential operators

L p approach to elliptic boundary value problems

Proof of Theorem 1

A priori estimates

Proof of Theorem 2

Proof of Theorem 3 - Part (i)

Proof of Theorem 3 - Part (ii)

Application to semilinear initial-boundary value problems.

Other Format:

Printed edition:

ISBN:

9783540466352

Access Restriction:

Restricted for use by site license.