Heat equation with strongly inhomogeneous noise

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:112

Article

Zähle, H

关键词: stochastic partial differential equation;    stochastic integral equation;    Martingale problem;    singular measure;    catalytic super-Brownian motion;   

DOI  :  10.1016/j.spa.2004.01.006

来源: Elsevier

【 摘 要 】

We consider the heat equation in dimension one with singular drift and inhomogeneous space-time white noise. In particular, the quadratic variation measure of the white noise is not required to be absolutely continuous w.r.t. the Lebesgue measure, neither in space nor in time. Under some assumptions we give statements on strong and weak existence as well as strong and weak uniqueness of continuous solutions. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

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