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}...
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AIMS Press
2020-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020144/fulltext.html |
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doaj-0e2ae47c80da4a8093e7f4715edf76402020-11-25T02:40:44ZengAIMS PressAIMS Mathematics2473-69882020-02-01532163219510.3934/math.2020144Rate of convergence of Euler approximation of time-dependent mixed SDEs driven by Brownian motions and fractional Brownian motionsWeiguo Liu0Yan Jiang1Zhi Li21 School of Statistics and Mathematics, Guangdong University of Finance & Economics, 21 Luntou Road, Guangzhou, Guangdong, MO 510320, P. R. China1 School of Statistics and Mathematics, Guangdong University of Finance & Economics, 21 Luntou Road, Guangzhou, Guangdong, MO 510320, P. R. China2 School of Information and Mathematics, Yangtze University, Jingzhou, Hubei, MO 434023, P. R. ChinaA 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.https://www.aimspress.com/article/10.3934/math.2020144/fulltext.htmlbrownian motionfractional brownian motioneuler approximationrate of convergence |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Weiguo Liu Yan Jiang Zhi Li |
| spellingShingle |
Weiguo Liu Yan Jiang Zhi Li Rate of convergence of Euler approximation of time-dependent mixed SDEs driven by Brownian motions and fractional Brownian motions AIMS Mathematics brownian motion fractional brownian motion euler approximation rate of convergence |
| author_facet |
Weiguo Liu Yan Jiang Zhi Li |
| author_sort |
Weiguo Liu |
| title |
Rate of convergence of Euler approximation of time-dependent mixed SDEs driven by Brownian motions and fractional Brownian motions |
| title_short |
Rate of convergence of Euler approximation of time-dependent mixed SDEs driven by Brownian motions and fractional Brownian motions |
| title_full |
Rate of convergence of Euler approximation of time-dependent mixed SDEs driven by Brownian motions and fractional Brownian motions |
| title_fullStr |
Rate of convergence of Euler approximation of time-dependent mixed SDEs driven by Brownian motions and fractional Brownian motions |
| title_full_unstemmed |
Rate of convergence of Euler approximation of time-dependent mixed SDEs driven by Brownian motions and fractional Brownian motions |
| title_sort |
rate of convergence of euler approximation of time-dependent mixed sdes driven by brownian motions and fractional brownian motions |
| publisher |
AIMS Press |
| series |
AIMS Mathematics |
| issn |
2473-6988 |
| publishDate |
2020-02-01 |
| description |
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. |
| topic |
brownian motion fractional brownian motion euler approximation rate of convergence |
| url |
https://www.aimspress.com/article/10.3934/math.2020144/fulltext.html |
| work_keys_str_mv |
AT weiguoliu rateofconvergenceofeulerapproximationoftimedependentmixedsdesdrivenbybrownianmotionsandfractionalbrownianmotions AT yanjiang rateofconvergenceofeulerapproximationoftimedependentmixedsdesdrivenbybrownianmotionsandfractionalbrownianmotions AT zhili rateofconvergenceofeulerapproximationoftimedependentmixedsdesdrivenbybrownianmotionsandfractionalbrownianmotions |
| _version_ |
1724780050790744064 |