Ratio limit theorems for a Brownian motion killed at the boundary of a Benedicks domain

• 成果类型: Article
• 署名作者: Collet, P; Martínez, S; San Martín, J
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Universidad de Chile
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1999
• 页码: 1160-1182
• 关键词: large time behavior; heat kernel

摘要

We consider a Brownian motion in a Benedicks domain with absorption at the boundary. We show ratio limit theorems for the associated heat kernel. When the hole is compact, therefore the Martin boundary is two dimensional; we obtain sharp estimates on the lifetime probabilities and we identify, in probabilistic terms, the various constants appearing in the theory.