Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion
成果类型：
Article
署名作者：
Chaumont, L; Doney, RA
署名单位：
Sorbonne Universite; University of Manchester
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s004400050216
发表日期：
1999
页码：
519-534
关键词：
摘要：
Any solution of the functional equation [GRAPHICS] where B is a Brownian motion, behaves like a reflected Brownian motion, except when it attains a new maximum: we call it an alpha-perturbed reflected Brownian motion. Similarly any solution of [GRAPHICS] behaves like a Brownian motion except when it attains a new maximum or minimum: we call it an alpha,beta-doubly perturbed Brownian motion. We complete some recent investigations by showing that for all permissible values of the parameters alpha, alpha and beta respectively, these equations have pathwise unique solutions, and these are adapted to the filtration of B.
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