Brownian motion and random walk perturbed at extrema

被引：0

作者：

Burgess Davis

机构：

[1] Statistics Department,

[2] Mathematical Sciences Buildings,undefined

[3] West Lafayette,undefined

[4] IN 47907-1399,undefined

[5] USA. e-mail:Purdue University,undefined

[6] bdavis@state.purdue.edu,undefined

来源：

Probability Theory and Related Fields | 1999年 / 113卷

关键词：

Mathematics Subject Classification (1991): 60F05, 60J15, 60J65, 82C41; Key words and phrases: Reinforced random walk – Perturbed Brownian motion;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let bt be Brownian motion. We show there is a unique adapted process xt which satisfies dxt = dbt except when xt is at a maximum or a minimum, when it receives a push, the magnitudes and directions of the pushes being the parameters of the process. For some ranges of the parameters this is already known. We show that if a random walk close to bt is perturbed properly, its paths are close to those of xt.

引用

页码：501 / 518

页数：17

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