Backward stochastic differential equations with nonlinear Young drivers II
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_ | 1866915481576800256 |
|---|---|
| author | Song, Jian Zhang, Huilin Zhang, Kuan |
| author_facet | Song, Jian Zhang, Huilin Zhang, Kuan |
| contents | This paper continues our previous work (Part I, arXiv:2504.18632v3) on the well-posedness of backward stochastic differential equations (BSDEs) involving a nonlinear Young integral of the form $\int_{t}^{T}g(Y_{r})η(dr,X_{r})$, with particular focus on the case where the driver $η(t,x)$ is unbounded. To address this setting, we develop a new localization method that extends solvability from BSDEs with bounded drivers to those with unbounded ones. As a direct application, we derive a nonlinear Feynman-Kac formula for a class of partial differential equations driven by Young signals (Young PDEs). Moreover, employing the proposed localization method, we obtain error estimates that compare Cauchy-Dirichlet problems on bounded domains with their whole-space Cauchy counterparts, with special attention to non-Lipschitz PDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Backward stochastic differential equations with nonlinear Young drivers II Song, Jian Zhang, Huilin Zhang, Kuan Probability 60L20, 60L50, 60H10 This paper continues our previous work (Part I, arXiv:2504.18632v3) on the well-posedness of backward stochastic differential equations (BSDEs) involving a nonlinear Young integral of the form $\int_{t}^{T}g(Y_{r})η(dr,X_{r})$, with particular focus on the case where the driver $η(t,x)$ is unbounded. To address this setting, we develop a new localization method that extends solvability from BSDEs with bounded drivers to those with unbounded ones. As a direct application, we derive a nonlinear Feynman-Kac formula for a class of partial differential equations driven by Young signals (Young PDEs). Moreover, employing the proposed localization method, we obtain error estimates that compare Cauchy-Dirichlet problems on bounded domains with their whole-space Cauchy counterparts, with special attention to non-Lipschitz PDEs. |
| title | Backward stochastic differential equations with nonlinear Young drivers II |
| topic | Probability 60L20, 60L50, 60H10 |
| url | https://arxiv.org/abs/2509.05183 |