Stochastic conformal integrators for linearly damped stochastic Poisson systems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908253496016896 |
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| author | Bréhier, Charles-Edouard Cohen, David Komori, Yoshio |
| author_facet | Bréhier, Charles-Edouard Cohen, David Komori, Yoshio |
| contents | We propose and study conformal integrators for linearly damped stochastic Poisson systems. We analyse the qualitative and quantitative properties of these numerical integrators: preservation of dynamics of certain Casimir and Hamiltonian functions, almost sure bounds of the numerical solutions, and strong and weak rates of convergence under appropriate conditions. These theoretical results are illustrated with several numerical experiments on, for example, the linearly damped free rigid body with random inertia tensor or the linearly damped stochastic Lotka--Volterra system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01540 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic conformal integrators for linearly damped stochastic Poisson systems Bréhier, Charles-Edouard Cohen, David Komori, Yoshio Numerical Analysis Probability 60H10, 60H35, 65C20, 65C30, 65P10 We propose and study conformal integrators for linearly damped stochastic Poisson systems. We analyse the qualitative and quantitative properties of these numerical integrators: preservation of dynamics of certain Casimir and Hamiltonian functions, almost sure bounds of the numerical solutions, and strong and weak rates of convergence under appropriate conditions. These theoretical results are illustrated with several numerical experiments on, for example, the linearly damped free rigid body with random inertia tensor or the linearly damped stochastic Lotka--Volterra system. |
| title | Stochastic conformal integrators for linearly damped stochastic Poisson systems |
| topic | Numerical Analysis Probability 60H10, 60H35, 65C20, 65C30, 65P10 |
| url | https://arxiv.org/abs/2503.01540 |