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arXiv · 1504.04631

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

Xiaoxia Xie·Jinqiao Duan·Xiaofan Li·Guangying Lv
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Abstract

Despite there are numerous theoretical studies of stochastic differential equations with a symmetric $α$-stable Lévy noise, very few regularity results exist in the case of $0<α\leq1$. 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 $α\in (0, 2]$.

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Xiaoxia Xie, Jinqiao Duan, Xiaofan Li, Guangying Lv. 2015-07-31. A regularity result for the nonlocal Fokker-Planck equation with Ornstein-Uhlenbeck drift. https://arxiv.org/abs/1504.04631

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