Brownian motion on the figure eight

被引：29

作者：

Grigorescu, I

Kang, M

机构：

[1] Univ Miami, Dept Math, Coral Gables, FL 33143 USA

[2] Northwestern Univ, Dept Math, Evanston, IL 60208 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2002年 / 15卷 / 03期

关键词：

absorbing Brownian motion; Laplace transform; decay rate; ergodicity;

D O I：

10.1023/A:1016232201962

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In an interval containing the origin we study a Brownian motion which returns to zero as soon as it reaches the boundary. We determine explicitly its transition probability, prove it is ergodic and calculate the decay rate to equilibrium. It is shown that the process solves the martingale problem for certain asymmetric boundary conditions and can be regarded as a diffusion on an eight shaped domain. In the case the origin is situated at a rationally commensurable distance from the two endpoints of the interval we give the complete characterization of the possibility of collapse of distinct paths.

引用

页码：817 / 844

页数：28