Abstract.
In the present paper we consider the transition semigroup P t related to some stochastic reaction-diffusion equations with the nonlinear term f having polynomial growth and satisfying some dissipativity conditions. We are proving that it has a regularizing effect in the Banach space of continuous functions , where ⊂ℝd is a bounded open set. In L 2() the only result proved is the strong Feller property, for d=1. Here we are able to prove that if f∈C ∞(ℝ) and d≤3, then for any and t>0. An important application is to the study of the ergodic properties of the system. These results are also of interest for some problem in stochastic control.
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Received: 20 August 1997 / Revised version: 27 May 1998
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Cerrai, S. Smoothing properties of transition semigroups relative to SDEs with values in Banach spaces. Probab Theory Relat Fields 113, 85–114 (1999). https://doi.org/10.1007/s004400050203
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DOI: https://doi.org/10.1007/s004400050203