Stochastic Domination of Exit Times for Random Walks and Brownian Motion with Drift
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910984618115072 |
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| author | Geng, Xi Markowsky, Greg |
| author_facet | Geng, Xi Markowsky, Greg |
| contents | 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. Peköz 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00277 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Domination of Exit Times for Random Walks and Brownian Motion with Drift Geng, Xi Markowsky, Greg Probability 60J65, 60G50 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. Peköz 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. |
| title | Stochastic Domination of Exit Times for Random Walks and Brownian Motion with Drift |
| topic | Probability 60J65, 60G50 |
| url | https://arxiv.org/abs/2408.00277 |