Boundary Value Problems and Markov Processes

• Main Author: Taira, Kazuaki. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Mathematics, 1499
• Subjects: Mathematics.; Operator theory.; Differential equations, partial.; Distribution (Probability theory).; Probability Theory and Stochastic Processes.; Operator Theory.; Partial Differential Equations.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-01677-6

This volume is devoted to a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an inte...

Table of Contents:

• 1 Semigroup Theory
• 2 Lp Theory of Pseudo-Differential Operators
• 3 Lp Approach to Elliptic Boundary Value Problems
• 4 Proof of Theorem 1
• 5 A Priori Estimates
• 6 Proof of Theorem 2
• 7 Proof of Theorem 3, Part (i)
• 8 Proof of Theorem 3, Part (ii)
• 9 Application to Semilinear Initial-Boundary Value Problems.