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Stochastic Averaging Principle for Two-Time-Scale SDEs with Distribution-Dependent Coefficients Driven by Fractional Brownian Motion
Guangjun Shen,
Jiayuan Yin,
Jiang-lun Wu
Communications in Mathematics and Statistics
Swansea University Author: Jiang-lun Wu
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DOI (Published version): 10.1007/s40304-023-00364-4
Abstract
In this paper, we derive an averaging principle for a fast-slow system of stochastic differential equations (SDEs) involving distribution dependent coefficients driven by both fractional Brownian motion (fBm) and standard Brownian motion (Bm). We first establish the existence and uniqueness of solut...
| Published in: | Communications in Mathematics and Statistics |
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| ISSN: | 2194-6701 2194-671X |
| Published: |
Springer Science and Business Media LLC
2023
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa63504 |
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| Abstract: |
In this paper, we derive an averaging principle for a fast-slow system of stochastic differential equations (SDEs) involving distribution dependent coefficients driven by both fractional Brownian motion (fBm) and standard Brownian motion (Bm). We first establish the existence and uniqueness of solutions of the fast-slow system and the corresponding averaging equation. Then, we show that the slow component strongly converges to the solution of the associated averaged equation. |
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| Keywords: |
Averaging principle, Fast–slow systems, Fractional Brownian motion, Standard Brownian motion |
| College: |
Faculty of Science and Engineering |
| Funders: |
This research is supported by the National Natural Science Foundation of China (12071003). |