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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.11815 |
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Table of Contents:
- Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from that in a finite interval with two absorbing boundaries. Here, we propose a method, which we refer to as a method of filtration, that allows us to construct the latter from only the knowledge of the former. We demonstrate that our method yields two solution forms, a method of eigenfunction expansion-like form and a method of image-like form. In particular, we argue that the latter solution form is a generalization of the method of image applicable to a stochastic process for which the method of image generally does not work, e.g., the Ornstein-Uhlenbeck process.