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White Noise Driven SPDEs with Reflection: Strong Feller Properties and Harnack Inequalities

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Abstract

In this paper, we prove that the strong Feller property holds for the solution of the white noise driven SPDEs with reflection. When the noise is additive, we establish some Harnack inequalities for the semigroup associated with the solution. As one of the applications, a Varadhan type small time asymptotics is obtained for the solution.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Henan Normal University, Xinxiang, Henan, China

    Tusheng Zhang

  2. School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

    Tusheng Zhang

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  1. Tusheng Zhang
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Correspondence to Tusheng Zhang.

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Zhang, T. White Noise Driven SPDEs with Reflection: Strong Feller Properties and Harnack Inequalities. Potential Anal 33, 137–151 (2010). https://doi.org/10.1007/s11118-009-9162-4

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  • DOI: https://doi.org/10.1007/s11118-009-9162-4

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