Integral identity and measure estimates for stationary Fokker-Planck equations

Abstract

We consider a Fokker-Planck equation in a general domain in ${\mathbb{R}}^n$ with $L_{\mathrm{loc}}^p$ drift term and $W_{\mathrm{loc}}^{1,p}$ 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.

Published at http://dx.doi.org/10.1214/14-AOP917 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Concentration and limit behaviors of stationary measures

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