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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/2510.21284 |
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| _version_ | 1866918169453527040 |
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| author | Kagan, Vincent Strickler, Edouard Villemonais, Denis |
| author_facet | Kagan, Vincent Strickler, Edouard Villemonais, Denis |
| contents | We consider a slow-fast stochastic process where the slow component is a jump process on a measurable index set whose transition rates depend on the position of the fast component. Between the jumps, the fast component evolves according to an ergodic dynamic in a state space determined by the index process. We prove that, when the ergodic dynamics are accelerated, the slow index process converges to an autonomous pure jump process on the index set. We apply our results to prove the convergence of a typed branching process toward a continuous-time Galton-Watson process, and of an epidemic model with fast viral loads dynamics to a standard contact process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Averaging principle for jump processes depending on fast ergodic dynamics Kagan, Vincent Strickler, Edouard Villemonais, Denis Probability We consider a slow-fast stochastic process where the slow component is a jump process on a measurable index set whose transition rates depend on the position of the fast component. Between the jumps, the fast component evolves according to an ergodic dynamic in a state space determined by the index process. We prove that, when the ergodic dynamics are accelerated, the slow index process converges to an autonomous pure jump process on the index set. We apply our results to prove the convergence of a typed branching process toward a continuous-time Galton-Watson process, and of an epidemic model with fast viral loads dynamics to a standard contact process. |
| title | Averaging principle for jump processes depending on fast ergodic dynamics |
| topic | Probability |
| url | https://arxiv.org/abs/2510.21284 |