White Noise Driven SPDEs with Reflection: Strong Feller Properties and Harnack Inequalities
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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.
KeywordsSPDEs with reflection Strong Feller property Comparison theorem Harnack inequalities Hyperbound property Varadhan type small time asymptotics
Mathematics Subject Classifications (2000)Primary 60H15; Secondary 60J60 31C25
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