## Illinois Journal of Mathematics

### Kolmogorov operator and Fokker–Planck equation associated to a stochastic Burgers equation driven by Lévy noise

#### Abstract

In this paper, we consider a stochastic Burgers equation driven by Lévy noise and study the transition semigroup of the solution to the initial value problem for the equation in the space of continuous functions weighted by a proper potential. We show that the infinitesimal generator is the closure of the Kolmogorov operator associated to the equation in a suitable topology. We also prove existence and uniqueness results for the associated Fokker–Planck equation.

#### Article information

Source
Illinois J. Math., Volume 58, Number 1 (2014), 167-205.

Dates
First available in Project Euclid: 1 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1427897173

Digital Object Identifier
doi:10.1215/ijm/1427897173

Mathematical Reviews number (MathSciNet)
MR3331846

Zentralblatt MATH identifier
1328.60148

Subjects
Primary: 34D08: Characteristic and Lyapunov exponents 34D25
Secondary: 60H20: Stochastic integral equations

#### Citation

Hu, Bing; Sun, Xiaobin; Xie, Yingchao. Kolmogorov operator and Fokker–Planck equation associated to a stochastic Burgers equation driven by Lévy noise. Illinois J. Math. 58 (2014), no. 1, 167--205. doi:10.1215/ijm/1427897173. https://projecteuclid.org/euclid.ijm/1427897173

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