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Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
Bin Pei,
Yong Xu,
Jiang-lun Wu 
Applied Mathematics Letters, Volume: 100, Start page: 106006
Swansea University Author:
Jiang-lun Wu
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DOI (Published version): 10.1016/j.aml.2019.106006
Abstract
In this paper, an averaging principle for multidimensional, time dependent, stochastic differential equations (SDEs) driven by fractional Brownian motion and standard Brownian motion was established. We combined the pathwise approach with the Itˆo stochastic calculus to handle both types of integral...
| Published in: | Applied Mathematics Letters |
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| ISSN: | 0893-9659 |
| Published: |
Elsevier BV
2020
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa51701 |
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| Abstract: |
In this paper, an averaging principle for multidimensional, time dependent, stochastic differential equations (SDEs) driven by fractional Brownian motion and standard Brownian motion was established. We combined the pathwise approach with the Itˆo stochastic calculus to handle both types of integrals involved and proved that the original SDEs can be approximated by averaged SDEs in the manner of mean square convergence and of convergence in probability, respectively. |
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| Keywords: |
Averaging principle, fractional Brownian motion, pathwise Riemann-Stieltjes integral, Itˆo stochastic calculus. |
| College: |
Faculty of Science and Engineering |
| Start Page: |
106006 |