The Kolmogorov operator associated to a Burgers SPDE in spaces of continuous functions

Details The Kolmogorov operator associated to a Burgers SPDE in spaces of continuous functions The Kolmogorov operator associated to a Burgers SPDE in spaces of continuous functions

2008-05-14

arxiv.org/abs/0805.2011v1

Mathematics

Analysis of PDEs

39 pages

Scientific paper

We are concerned with a viscous Burgers equation forced by a perturbation of white noise type. We study the corresponding transition semigroup in a space of continuous functions weighted by a proper potential, and we show that the infinitesimal generator is the closure (with respect to a suitable topology) of the Kolmogorov operator associated to the stochastic equation. In the last part of the paper we use this result to solve the corresponding Fokker-Planck equation.

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