A regularity result for the nonlocal Fokker-Planck equation with Ornstein-Uhlenbeck drift

Abstract

Despite there are numerous theoretical studies of stochastic differential equations with a symmetric $\alpha$-stable Lévy noise, very few regularity results exist in the case of $0<\alpha \le 1$. In this paper, we study the fractional Fokker-Planck equation with Ornstein-Uhlenbeck drift, and prove that there exists a unique solution, which is $C^{\infty }$ in space for $t>0$ when $\alpha \in (0,2]$.

6 pages

References in corpus (1)

• Fokker-Planck Equations for Stochastic Dynamical Systems with Symmetric Lévy Motions

Cited by in corpus (3)

• BMO estimates for stochastic singular integral operators and its application to PDEs with Lévy noise
• Regularity of stochastic nonlocal diffusion equations
• Morrey-Campanato estimates for the moments of stochastic integral operators and its application to SPDEs