Time-reversal and elliptic boundary value problems

Zhen Qing Chen; Tusheng Zhang

doi:10.1214/08-AOP427

Time-reversal and elliptic boundary value problems

Zhen Qing Chen, Tusheng Zhang

科研成果: 期刊稿件 › 文章 › 同行评审

19 引用（Scopus）

摘要

In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have the maximum principle. Our method is probabilistic. The time reversal of symmetric Markov processes and the theory of Dirichlet forms play a crucial role in our approach.

源语言	英语
页（从-至）	1008-1043
页数	36
期刊	Annals of Probability
卷	37
期	3
DOI	https://doi.org/10.1214/08-AOP427
出版状态	已出版 - 5月 2009
已对外发布	是

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Chen, Z. Q., & Zhang, T. (2009). Time-reversal and elliptic boundary value problems. Annals of Probability, 37(3), 1008-1043. https://doi.org/10.1214/08-AOP427

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keywords = "Boundary value problem, Diffusion, Feynman-kac transform, Girsanov transform, Multiplicative functional, Partial differential equation, Probabilistic representation, Quadratic form, Time-reversal, Weak solution",

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KW - Boundary value problem

KW - Diffusion

KW - Feynman-kac transform

KW - Girsanov transform

KW - Multiplicative functional

KW - Partial differential equation

KW - Probabilistic representation

KW - Quadratic form

KW - Time-reversal

KW - Weak solution

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Time-reversal and elliptic boundary value problems

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