The Euler-Maruyama method for invariant measures of McKean-Vlasov stochastic differential equations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914478967226368 |
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| author | Wang, Zhen Wu, Mingyan |
| author_facet | Wang, Zhen Wu, Mingyan |
| contents | This paper investigates the approximation of invariant measures for McKean-Vlasov stochastic differential equations (SDEs) using the Euler-Maruyama (EM) scheme under a monotonicity condition. Firstly, the convergence of the numerical solution from the EM scheme to its continuous-time counterpart is established. Secondly, we show that the numerical solution admits a unique invariant measure and derive its convergence rate under the Wasserstein metric. In parallel, it is demonstrated that the associated particle system also possesses these properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14543 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Euler-Maruyama method for invariant measures of McKean-Vlasov stochastic differential equations Wang, Zhen Wu, Mingyan Probability This paper investigates the approximation of invariant measures for McKean-Vlasov stochastic differential equations (SDEs) using the Euler-Maruyama (EM) scheme under a monotonicity condition. Firstly, the convergence of the numerical solution from the EM scheme to its continuous-time counterpart is established. Secondly, we show that the numerical solution admits a unique invariant measure and derive its convergence rate under the Wasserstein metric. In parallel, it is demonstrated that the associated particle system also possesses these properties. |
| title | The Euler-Maruyama method for invariant measures of McKean-Vlasov stochastic differential equations |
| topic | Probability |
| url | https://arxiv.org/abs/2604.14543 |