Backward stochastic differential equations with nonlinear Young drivers I
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_ | 1866911085157679104 |
|---|---|
| author | Song, Jian Zhang, Huilin Zhang, Kuan |
| author_facet | Song, Jian Zhang, Huilin Zhang, Kuan |
| contents | This paper (alongside its companion, Part II \cite{BSDEYoung-II}) investigates backward stochastic differential equations (BSDEs) involving a nonlinear Young integral of the form $\int_{t}^{T}g(Y_{r})η(dr,X_{r})$, where the driver $η(t,x)$ is a space-time Hölder continuous function and $X$ is a diffusion process. Solutions to such equations provide a probabilistic interpretation of the solutions to stochastic partial differential equations (SPDEs) driven by space-time noise.
Assuming the driver $η(t,x)$ is bounded, we establish the existence and uniqueness of the solutions to these BSDEs via a modified Picard iteration method. We then derive a comparison principle by analyzing the associated linear BSDEs and establish regularity properties of the solutions. As an application, we obtain Feynman-Kac formulae for a class of linear stochastic heat equations subject to Neumann boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Backward stochastic differential equations with nonlinear Young drivers I Song, Jian Zhang, Huilin Zhang, Kuan Probability Analysis of PDEs Classical Analysis and ODEs 60L20, 60L50, 60H10 This paper (alongside its companion, Part II \cite{BSDEYoung-II}) investigates backward stochastic differential equations (BSDEs) involving a nonlinear Young integral of the form $\int_{t}^{T}g(Y_{r})η(dr,X_{r})$, where the driver $η(t,x)$ is a space-time Hölder continuous function and $X$ is a diffusion process. Solutions to such equations provide a probabilistic interpretation of the solutions to stochastic partial differential equations (SPDEs) driven by space-time noise. Assuming the driver $η(t,x)$ is bounded, we establish the existence and uniqueness of the solutions to these BSDEs via a modified Picard iteration method. We then derive a comparison principle by analyzing the associated linear BSDEs and establish regularity properties of the solutions. As an application, we obtain Feynman-Kac formulae for a class of linear stochastic heat equations subject to Neumann boundary conditions. |
| title | Backward stochastic differential equations with nonlinear Young drivers I |
| topic | Probability Analysis of PDEs Classical Analysis and ODEs 60L20, 60L50, 60H10 |
| url | https://arxiv.org/abs/2504.18632 |