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July 2015 Integral identity and measure estimates for stationary Fokker–Planck equations
Wen Huang, Min Ji, Zhenxin Liu, Yingfei Yi
Ann. Probab. 43(4): 1712-1730 (July 2015). DOI: 10.1214/14-AOP917


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.


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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.


Received: 1 December 2013; Revised: 1 January 2014; Published: July 2015
First available in Project Euclid: 3 June 2015

zbMATH: 1319.35268
MathSciNet: MR3353813
Digital Object Identifier: 10.1214/14-AOP917

Primary: 35Q84 , 60J60
Secondary: 37B25

Keywords: Fokker–Planck equation , integral identity , level set method , measure estimates , Stationary measures

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.43 • No. 4 • July 2015
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