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Heat equation with strongly inhomogeneous noise

  • The author considers 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 the author gives statements on strong and weak existence as well as strong and weak uniqueness of continuous solutions.

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Author:Henryk Zähle
Document Type:Article
Year of first Publication:2004
Year of Completion:2004
Release Date:2017/03/24
Source:Stochastic Processes and their Applications. - 112 (2004), 1, S. 95 - 118
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert