Stochastic theta methods for random periodic solution of stochastic differential equations under non-globally Lipschitz conditions
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909227539234816 |
|---|---|
| author | Chen, Ziheng Cao, Liangmin Chen, Lin |
| author_facet | Chen, Ziheng Cao, Liangmin Chen, Lin |
| contents | This work focuses on the numerical approximations of random periodic solutions of stochastic differential equations (SDEs). Under non-globally Lipschitz conditions, we prove the existence and uniqueness of random periodic solutions for the considered equations and its numerical approximations generated by the stochastic theta (ST) methods with theta within (1/2,1]. It is shown that the random periodic solution of each ST method converges strongly in the mean square sense to that of SDEs for all step size. More precisely, the mean square convergence order is 1/2 for SDEs with multiplicative noise and 1 for SDEs with additive noise. Numerical results are finally reported to confirm these theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic theta methods for random periodic solution of stochastic differential equations under non-globally Lipschitz conditions Chen, Ziheng Cao, Liangmin Chen, Lin Numerical Analysis This work focuses on the numerical approximations of random periodic solutions of stochastic differential equations (SDEs). Under non-globally Lipschitz conditions, we prove the existence and uniqueness of random periodic solutions for the considered equations and its numerical approximations generated by the stochastic theta (ST) methods with theta within (1/2,1]. It is shown that the random periodic solution of each ST method converges strongly in the mean square sense to that of SDEs for all step size. More precisely, the mean square convergence order is 1/2 for SDEs with multiplicative noise and 1 for SDEs with additive noise. Numerical results are finally reported to confirm these theoretical findings. |
| title | Stochastic theta methods for random periodic solution of stochastic differential equations under non-globally Lipschitz conditions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.09747 |