Rate of convergence of Euler approximation of time-dependent mixed SDEs driven by Brownian motions and fractional Brownian motions
A kind of time-dependent mixed stochastic differential equations driven by Brownian motions and fractional Brownian motions with Hurst parameter $H>\frac{1}{2}$ is considered. We prove that the rate of convergence of Euler approximation of the solutions can be estimated by $O(\delta^{\frac{1}...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-02-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020144/fulltext.html |
| Summary: | A kind of time-dependent mixed stochastic differential equations driven by Brownian motions and fractional Brownian motions with Hurst parameter $H>\frac{1}{2}$ is considered. We prove that the rate of convergence of Euler approximation of the solutions can be estimated by $O(\delta^{\frac{1}{2}\wedge(2H-1)})$ in probability, where $\delta$ is the diameter of the partition used for discretization. |
|---|---|
| ISSN: | 2473-6988 |