Probabilistic representation of ODE solutions with quantitative estimates
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915605143093248 |
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| author | Huang, Qiao Privault, Nicolas |
| author_facet | Huang, Qiao Privault, Nicolas |
| contents | This paper considers the probabilistic representation of the solutions of ordinary differential equations (ODEs) by the generation of marked random trees in which marks can be interpreted as mutant types in population genetics models. We present sufficient conditions on equation coefficients that ensure the integrability and uniform integrability of the functionals of random trees used in this representation. Those conditions rely on the analysis of a marked branching process that controls the growth of random trees and provide implicit lower bounds on the explosion time of the underlying ODE, thus providing a connection between branching process explosion and the existence and uniqueness of ODE solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probabilistic representation of ODE solutions with quantitative estimates Huang, Qiao Privault, Nicolas Probability Classical Analysis and ODEs 65L06, 34A25, 34-04, 05C05, 65C05 This paper considers the probabilistic representation of the solutions of ordinary differential equations (ODEs) by the generation of marked random trees in which marks can be interpreted as mutant types in population genetics models. We present sufficient conditions on equation coefficients that ensure the integrability and uniform integrability of the functionals of random trees used in this representation. Those conditions rely on the analysis of a marked branching process that controls the growth of random trees and provide implicit lower bounds on the explosion time of the underlying ODE, thus providing a connection between branching process explosion and the existence and uniqueness of ODE solutions. |
| title | Probabilistic representation of ODE solutions with quantitative estimates |
| topic | Probability Classical Analysis and ODEs 65L06, 34A25, 34-04, 05C05, 65C05 |
| url | https://arxiv.org/abs/2502.10644 |