Integral identity and measure estimates for stationary Fokker–Planck equations

Huang, Wen ^[1] ; Ji, Min ^[2] ; Yi, Yingfei. ^[3] ; Zhenxin Liu
1. [1] University of Science and Technology of China
  
  University of Science and Technology of China
  
  China
2. [2] Chinese Academy of Science and Technology for Development
  
  Chinese Academy of Science and Technology for Development
  
  China
3. [3] Jilin University
  
  Jilin University
  
  China
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Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 4, 2015, págs. 1712-1730
Idioma: inglés
DOI: 10.1214/14-AOP917
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Resumen
- We consider a Fokker–Planck equation in a general domain in Rn with Lploc drift term and W1,ploc 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.