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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.02700 |
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| _version_ | 1866918114152677376 |
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| author | Ávila-Vales, Eric José Villa-Morales, José |
| author_facet | Ávila-Vales, Eric José Villa-Morales, José |
| contents | Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the distribution of exit times of the stochastic process within a bounded domain. These quantities are obtained by solving elliptic and parabolic partial differential equations (PDEs), respectively. To support practical applications, we propose a numerical scheme implemented in FreeFEM, emphasizing its effectiveness in two- and three-dimensional cases due to the software's limitations in higher dimensions. The examples provided illustrate the theoretical results, which extend known one-dimensional solutions to higher-dimensional settings. This contribution bridges theoretical and computational approaches for analyzing stochastic processes in multidimensional domains, offering insights into their behavior and potential applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some stochastic process techniques applied to deterministic models Ávila-Vales, Eric José Villa-Morales, José Probability 35B09, 60G53, 92B05, 65M06 Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the distribution of exit times of the stochastic process within a bounded domain. These quantities are obtained by solving elliptic and parabolic partial differential equations (PDEs), respectively. To support practical applications, we propose a numerical scheme implemented in FreeFEM, emphasizing its effectiveness in two- and three-dimensional cases due to the software's limitations in higher dimensions. The examples provided illustrate the theoretical results, which extend known one-dimensional solutions to higher-dimensional settings. This contribution bridges theoretical and computational approaches for analyzing stochastic processes in multidimensional domains, offering insights into their behavior and potential applications. |
| title | Some stochastic process techniques applied to deterministic models |
| topic | Probability 35B09, 60G53, 92B05, 65M06 |
| url | https://arxiv.org/abs/2508.02700 |