Parameter-related strong convergence rates of Euler-type methods for time-changed stochastic differential equations
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918382550384640 |
|---|---|
| author | Zuo, Ruchun |
| author_facet | Zuo, Ruchun |
| contents | An Euler-type framework with equidistant step sizes is proposed for a class of time-changed stochastic differential equations.We establish the strong convergence rate of the standard Euler--Maruyama method under the global Lipschitz condition.The theoretical analysis is then extended to the truncated Euler--Maruyama method, proving its strong convergence under relaxed Khasminskii-type conditions.For both numerical schemes, the strong convergence orders are explicitly shown to be close to $α/2$, where $α\in (0,1)$ is the parameter of the time-change process.These results are significantly different from existing works using random step sizes, which typically preserve the classical convergence order of $1/2$.Numerical simulations are provided to demonstrate the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parameter-related strong convergence rates of Euler-type methods for time-changed stochastic differential equations Zuo, Ruchun Numerical Analysis Probability An Euler-type framework with equidistant step sizes is proposed for a class of time-changed stochastic differential equations.We establish the strong convergence rate of the standard Euler--Maruyama method under the global Lipschitz condition.The theoretical analysis is then extended to the truncated Euler--Maruyama method, proving its strong convergence under relaxed Khasminskii-type conditions.For both numerical schemes, the strong convergence orders are explicitly shown to be close to $α/2$, where $α\in (0,1)$ is the parameter of the time-change process.These results are significantly different from existing works using random step sizes, which typically preserve the classical convergence order of $1/2$.Numerical simulations are provided to demonstrate the theoretical findings. |
| title | Parameter-related strong convergence rates of Euler-type methods for time-changed stochastic differential equations |
| topic | Numerical Analysis Probability |
| url | https://arxiv.org/abs/2510.16405 |