Abstract
We consider a Fokker–Planck equation in a general domain in $\mathbb{R}^{n}$ with $L^{p}_{\mathrm{loc}}$ drift term and $W^{1,p}_{\mathrm{loc}}$ diffusion term for any $p>n$. By deriving an integral identity, we give several measure estimates of regular stationary measures in an exterior domain with respect to diffusion and Lyapunov-like or anti-Lyapunov-like functions. These estimates will be useful to problems such as the existence and nonexistence of stationary measures in a general domain as well as the concentration and limit behaviors of stationary measures as diffusion vanishes.
Citation
Wen Huang. Min Ji. Zhenxin Liu. Yingfei Yi. "Integral identity and measure estimates for stationary Fokker–Planck equations." Ann. Probab. 43 (4) 1712 - 1730, July 2015. https://doi.org/10.1214/14-AOP917
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