Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909078482059264 |
|---|---|
| author | Deng, Chang-Song Huang, Xing |
| author_facet | Deng, Chang-Song Huang, Xing |
| contents | We establish the well-posedness for a class of McKean-Vlasov SDEs driven by symmetric $α$-stable Lévy process ($1/2<α\leq1$), where the drift coefficient is Hölder continuous in space variable, while the noise coefficient is Lipscitz continuous in space variable, and both of them satisfy the Lipschitz condition in distribution variable with respect to Wasserstein distance. If the drift coefficient does not depend on distribution variable, our methodology developed in this paper applies to the case $α\in(0,1]$. The main tool relies on heat kernel estimates for (distribution independent) stable SDEs and Banach's fixed point theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11384 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises Deng, Chang-Song Huang, Xing Probability We establish the well-posedness for a class of McKean-Vlasov SDEs driven by symmetric $α$-stable Lévy process ($1/2<α\leq1$), where the drift coefficient is Hölder continuous in space variable, while the noise coefficient is Lipscitz continuous in space variable, and both of them satisfy the Lipschitz condition in distribution variable with respect to Wasserstein distance. If the drift coefficient does not depend on distribution variable, our methodology developed in this paper applies to the case $α\in(0,1]$. The main tool relies on heat kernel estimates for (distribution independent) stable SDEs and Banach's fixed point theorem. |
| title | Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises |
| topic | Probability |
| url | https://arxiv.org/abs/2401.11384 |