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Log-Harnack inequality for mild solutions of SPDEs with multiplicative noise. (English) Zbl 1285.60065
Summary: Due to technical reasons, existing results concerning Harnack type inequalities for stochastic partial differential equation (SPDEs) with multiplicative noise apply only to the case where the coefficient in the noise term is a Hilbert-Schmidt perturbation of a constant bounded operator. In this paper, we obtain gradient estimates, a log-Harnack inequality for mild solutions of general SPDEs with multiplicative noise whose coefficient is even allowed to be unbounded which cannot be Hilbert-Schmidt. Applications to stochastic reaction-diffusion equations driven by space-time white noise are presented.

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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##### References:
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