Long Time $\W_0$-$\widetilde{\W}_1$ type Propagation of Chaos for Mean Field Interacting Particle System
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910568578809856 |
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| author | Huang, Xing Yang, Fen-Fen Yuan, Chenggui |
| author_facet | Huang, Xing Yang, Fen-Fen Yuan, Chenggui |
| contents | In this paper, a general result on the long time $\W_0$-$\widetilde{\W}_1$ type propagation of chaos, propagation of chaos with regularization effect, for mean field interacting particle system driven by Lévy noise is derived, where $\W_0$ is one half of the total variation distance while $\widetilde{\W}_1$ is the $L^1$-Wasserstein distance. By using the method of coupling, the general result is applied to mean field interacting particle system driven by multiplicative Brownian motion and additive $α(α>1)$-stable noise respectively, where the non-interacting drift is assumed to be dissipative in long distance and the initial distribution of interacting particle system converges to that of the limit equation in $\widetilde{\W}_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01795 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Long Time $\W_0$-$\widetilde{\W}_1$ type Propagation of Chaos for Mean Field Interacting Particle System Huang, Xing Yang, Fen-Fen Yuan, Chenggui Probability In this paper, a general result on the long time $\W_0$-$\widetilde{\W}_1$ type propagation of chaos, propagation of chaos with regularization effect, for mean field interacting particle system driven by Lévy noise is derived, where $\W_0$ is one half of the total variation distance while $\widetilde{\W}_1$ is the $L^1$-Wasserstein distance. By using the method of coupling, the general result is applied to mean field interacting particle system driven by multiplicative Brownian motion and additive $α(α>1)$-stable noise respectively, where the non-interacting drift is assumed to be dissipative in long distance and the initial distribution of interacting particle system converges to that of the limit equation in $\widetilde{\W}_1$. |
| title | Long Time $\W_0$-$\widetilde{\W}_1$ type Propagation of Chaos for Mean Field Interacting Particle System |
| topic | Probability |
| url | https://arxiv.org/abs/2404.01795 |