## The Annals of Applied Probability

### On Weak Convergence of Conditional Survival Measure of One-Dimensional Brownian Motion with a Drift

Tobias Povel

#### 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

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