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Heat equation with strongly inhomogeneous noise

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  • Zähle, Henryk

Abstract

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.

Suggested Citation

  • Zähle, Henryk, 2004. "Heat equation with strongly inhomogeneous noise," Stochastic Processes and their Applications, Elsevier, vol. 112(1), pages 95-118, July.
    • Handle: RePEc:eee:spapps:v:112:y:2004:i:1:p:95-118
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