THE SNAPPING OUT BROWNIAN MOTION

• 成果类型: Article
• 署名作者: Lejay, Antoine
• 署名单位: Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Inria; Universite de Lorraine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1131
• 发表日期: 2016
• 页码: 1727-1742
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; dimensional diffusion-processes; boundary-conditions; discontinuous coefficients; MARKOV-PROCESSES; euler scheme; simulation; graphs

摘要

We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at 0 with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier. For this, we use a process called here the snapping out Brownian motion, whose properties are studied. As this construction is motivated by applications, for example, in brain imaging or in chemistry, a simulation scheme is also provided.