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Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
Guangjun Shen,
Jie Xiang 
,
Jiang-lun Wu
,
Jiang-lun Wu
Journal of Differential Equations, Volume: 321, Pages: 381 - 414
Swansea University Author:
Jiang-lun Wu
-
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DOI (Published version): 10.1016/j.jde.2022.03.015
Abstract
In this paper, we study distribution dependent stochastic differential equations driven simultaneously by fractional Brownian motion with Hurst index H > 1/2 and standard Brownian motion. We first establish the existence and uniqueness theorem for solutions of the distribution dependent stochasti...
| Published in: | Journal of Differential Equations |
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| ISSN: | 0022-0396 |
| Published: |
Elsevier BV
2022
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa59426 |
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| Abstract: |
In this paper, we study distribution dependent stochastic differential equations driven simultaneously by fractional Brownian motion with Hurst index H > 1/2 and standard Brownian motion. We first establish the existence and uniqueness theorem for solutions of the distribution dependent stochastic differential equations by utilising the Carath\'eodory approximation. We then show that, under certain averaging condition, the solutions of distribution dependent stochastic differential equations can be approximated by the solutions of the associated averaged distribution dependent stochastic differential equations in the sense of the mean square convergence. |
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| Keywords: |
Distribution dependent stochastic differential equations; fractional Brow- nian motion; stochastic averaging principle. |
| College: |
Faculty of Science and Engineering |
| Start Page: |
381 |
| End Page: |
414 |