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arXiv · 2408.00277

Stochastic Domination of Exit Times for Random Walks and Brownian Motion with Drift

Xi Geng·Greg Markowsky
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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.

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Xi Geng, Greg Markowsky. 2024-08-01. Stochastic Domination of Exit Times for Random Walks and Brownian Motion with Drift. https://arxiv.org/abs/2408.00277

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