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February, 1995 On Weak Convergence of Conditional Survival Measure of One-Dimensional Brownian Motion with a Drift
Tobias Povel
Ann. Appl. Probab. 5(1): 222-238 (February, 1995). DOI: 10.1214/aoap/1177004837

Abstract

We consider a one-dimensional Brownian motion with a constant drift, moving among Poissonian obstacles. In the case where the drift is below some critical value we characterize the limiting distribution of the process under the conditional probability measure that the particle has survived up to time $t$. Unlike the situation where the drift equals zero, we show in particular that in the presence of a constant drift, the process in natural scale feels the "boundary."

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Tobias Povel. "On Weak Convergence of Conditional Survival Measure of One-Dimensional Brownian Motion with a Drift." Ann. Appl. Probab. 5 (1) 222 - 238, February, 1995. https://doi.org/10.1214/aoap/1177004837

Information

Published: February, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0822.60094
MathSciNet: MR1325050
Digital Object Identifier: 10.1214/aoap/1177004837

Subjects:
Primary: 60K40
Secondary: 82D30

Keywords: Brownian motion with drift , survival measure , taboo measure , weak convergence

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 1 • February, 1995
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