The Kolmogorov Operator Associated to a Burgers SPDE in Spaces of Continuous Functions

作者：Manca Luigi^*

来源：Potential Analysis, 2010, 32(1): 67-99.

DOI：10.1007/s11118-009-9146-4

• Burgers equation
• White noise
• Kolmogorov operator
• Transition semigroup
• Fokker-Planck equation

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.

• 出版日期2010-1