Explicit numerical approximations for McKean-Vlasov stochastic differential equations in finite and infinite time
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909975008247808 |
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| author | Cui, Yuanping Li, Xiaoyue Liu, Yi Wang, Fengyu |
| author_facet | Cui, Yuanping Li, Xiaoyue Liu, Yi Wang, Fengyu |
| contents | Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes the theory on the propagation of chaos in the Lq sense. The optimal uniform-in-time strong convergence rate 1/2-order of the numerical solutions is obtained for the interacting particle system. Furthermore, it is proved that the numerical solutions capture the long-term dynamical behaviors of MV-SDEs precisely, including moment boundedness, stability, and ergodicity. Moreover, a unique numerical invariant probability measure is yielded, which converges to the underlying invariant probability measure of MV-SDEs in the L2-Wasserstein distance. Finally, several numerical experiments are carried out to support the main results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02878 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit numerical approximations for McKean-Vlasov stochastic differential equations in finite and infinite time Cui, Yuanping Li, Xiaoyue Liu, Yi Wang, Fengyu Probability Numerical Analysis Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes the theory on the propagation of chaos in the Lq sense. The optimal uniform-in-time strong convergence rate 1/2-order of the numerical solutions is obtained for the interacting particle system. Furthermore, it is proved that the numerical solutions capture the long-term dynamical behaviors of MV-SDEs precisely, including moment boundedness, stability, and ergodicity. Moreover, a unique numerical invariant probability measure is yielded, which converges to the underlying invariant probability measure of MV-SDEs in the L2-Wasserstein distance. Finally, several numerical experiments are carried out to support the main results. |
| title | Explicit numerical approximations for McKean-Vlasov stochastic differential equations in finite and infinite time |
| topic | Probability Numerical Analysis |
| url | https://arxiv.org/abs/2401.02878 |