Stochastic Domination of Exit Times for Random Walks and Brownian Motion with Drift
Probability
2025-06-05 v2
Abstract
In this note, by an elementary use of Girsanov's transform we show that the exit time for either a biased random walk or a drifted Brownian motion on a symmetric interval is stochastically monotone with respect to the drift parameter. In the random walk case, this gives an alternative proof of a recent result of E. Pek\"oz and R. Righter in 2024. Our arguments in both discrete and continuous cases are parallel to each other. We also outline a simple SDE proof for the Brownian case based on a standard comparison theorem.
Keywords
Cite
@article{arxiv.2408.00277,
title = {Stochastic Domination of Exit Times for Random Walks and Brownian Motion with Drift},
author = {Xi Geng and Greg Markowsky},
journal= {arXiv preprint arXiv:2408.00277},
year = {2025}
}