SOME STOCHASTIC PROCESS WITHOUT BIRTH, LINKED TO THE MEAN CURVATURE FLOW

• 成果类型: Article
• 署名作者: Coulibaly-Pasquier, Kolehe A.
• 署名单位: University of Luxembourg
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP580
• 发表日期: 2011
• 页码: 1305-1331
• 关键词: level sets; motion; time

摘要

Using Huisken's results about the mean curvature flow on a strictly convex hypersurface and Kendall-Cranston's coupling, we will build a stochastic process without birth and show that there exists a unique law of such a process. This process has many similarities with the circular Brownian motion studied by Emery and Schachermayer, and Arnaudon. In general this process is not a stationary process; it is linked to some differential equation without initial condition. We will show that this differential equation has a unique solution up to a multiplicative constant.