Spinning Brownian motion

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Duarte, Mauricio A.

关键词: Stationary distribution;    Stochastic differential equations;    Excursion theory;    Degenerate reflected diffusion;   

DOI  :  10.1016/j.spa.2015.06.005

来源: Elsevier

【 摘 要 】

We prove strong existence and uniqueness for a reflection process X in a smooth, bounded domain D that behaves like obliquely-reflected-Brownian-motion, except that the direction of reflection depends on a (spin) parameter S, which only changes when X is on the boundary of D according to a physical rule. The process (X, S) is a degenerate diffusion. We show uniqueness of the stationary distribution by using techniques based on excursions of X from partial derivative D, and an associated exit system. We also show that the process admits a submartingale formulation and use related results to show examples of the stationary distribution. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free