Mean-field backward stochastic Volterra integral equations: well-posedness and related particle system
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909896344076288 |
|---|---|
| author | Hao, Tao Hu, Ying Wen, Jiaqiang |
| author_facet | Hao, Tao Hu, Ying Wen, Jiaqiang |
| contents | This paper studies the mean-field backward stochastic Volterra integral equations (mean-field BSVIEs) and associated particle systems. We establish the existence and uniqueness of solutions to mean-field BSVIEs when the generator $g$ is of linear growth or quadratic growth with respect to $Z$, respectively. Moreover, the propagation of chaos is analyzed for the corresponding particle systems under two conditions. When $g$ is of linear growth in $Z$, the convergence rate is proven to be of order $\mathscr{Q}(N)$. When $g$ is of quadratic growth in $Z$ and is independent of the law of $Z$, we not only establish the convergence of the particle systems but also derive a convergence rate of order $\mathscr{O}(N^{-\frac{1}{2λ}})$, where $λ>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean-field backward stochastic Volterra integral equations: well-posedness and related particle system Hao, Tao Hu, Ying Wen, Jiaqiang Probability 60H10, 60H30 This paper studies the mean-field backward stochastic Volterra integral equations (mean-field BSVIEs) and associated particle systems. We establish the existence and uniqueness of solutions to mean-field BSVIEs when the generator $g$ is of linear growth or quadratic growth with respect to $Z$, respectively. Moreover, the propagation of chaos is analyzed for the corresponding particle systems under two conditions. When $g$ is of linear growth in $Z$, the convergence rate is proven to be of order $\mathscr{Q}(N)$. When $g$ is of quadratic growth in $Z$ and is independent of the law of $Z$, we not only establish the convergence of the particle systems but also derive a convergence rate of order $\mathscr{O}(N^{-\frac{1}{2λ}})$, where $λ>1$. |
| title | Mean-field backward stochastic Volterra integral equations: well-posedness and related particle system |
| topic | Probability 60H10, 60H30 |
| url | https://arxiv.org/abs/2511.07173 |