Existence of the Fomin derivative of the invariant measure of a stochastic reaction--diffusion equation

2015/02/26 by Giuseppe Da Prato, Arnaud Debussche, Da Prato, Giuseppe +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1502.07490

arxiv created 2015/02/26 · arxiv updated 2015/02/27

Abstract

We consider a reaction--diffusion equation perturbed by noise (not necessarily white). We prove existence of the Fomin derivative of the corresponding transition semigroup P_t. The main tool is a new estimate for P_tDφ in terms of ‖φ‖_L²(H,ν), where ν is the invariant measure of P_t.

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