The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 5, Number 1 (1995), 222-238.
On Weak Convergence of Conditional Survival Measure of One-Dimensional Brownian Motion with a Drift
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."
Article information
Source
Ann. Appl. Probab., Volume 5, Number 1 (1995), 222-238.
Dates
First available in Project Euclid: 19 April 2007
Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004837
Digital Object Identifier
doi:10.1214/aoap/1177004837
Mathematical Reviews number (MathSciNet)
MR1325050
Zentralblatt MATH identifier
0822.60094
JSTOR
links.jstor.org
Subjects
Primary: 60K40: Other physical applications of random processes
Secondary: 82D30: Random media, disordered materials (including liquid crystals and spin glasses)
Keywords
Brownian motion with drift survival measure weak convergence taboo measure
Citation
Povel, Tobias. On Weak Convergence of Conditional Survival Measure of One-Dimensional Brownian Motion with a Drift. Ann. Appl. Probab. 5 (1995), no. 1, 222--238. doi:10.1214/aoap/1177004837. https://projecteuclid.org/euclid.aoap/1177004837
