The Annals of Probability

Ratio Limit Theorems for a Brownian Motion Killed at the Boundary of a Benedicks Domain

Pierre Collet, Servet Martínez, and Jaime San Martín

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Abstract

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.

Article information

Source
Ann. Probab. Volume 27, Number 3 (1999), 1160-1182.

Dates
First available in Project Euclid: 29 May 2002

Permanent link to this document
http://projecteuclid.org/euclid.aop/1022677443

Digital Object Identifier
doi:10.1214/aop/1022677443

Mathematical Reviews number (MathSciNet)
MR1733144

Zentralblatt MATH identifier
0965.60076

Subjects
Primary: 60J65: Brownian motion [See also 58J65] 35B40 35K05

Keywords
Brownian motion heat kernel ratio limit theorems Benedicks domain

Citation

Collet, Pierre; Martínez, Servet; San Martín, Jaime. Ratio Limit Theorems for a Brownian Motion Killed at the Boundary of a Benedicks Domain. Ann. Probab. 27 (1999), no. 3, 1160--1182. doi:10.1214/aop/1022677443. http://projecteuclid.org/euclid.aop/1022677443.


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