Stationary distributions for diffusions with inert drift

• 成果类型: Article
• 署名作者: Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing; Hairer, Martin
• 署名单位: University of Washington; University of Washington Seattle; University of Connecticut; University of Warwick
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0182-6
• 发表日期: 2010
• 页码: 1-47
• 关键词: reflecting brownian-motion; CONVERGENCE; uniqueness; EQUATIONS

摘要

Consider reflecting Brownian motion in a bounded domain in R-d that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential.