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On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions
Guangjun Shen,
Tingting Zhang,
Jie Song,
Jiang-lun Wu
Applied Mathematics and Optimization, Volume: 88, Issue: 2
Swansea University Author: Jiang-lun Wu
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DOI (Published version): 10.1007/s00245-023-10007-3
Abstract
In this paper, a class of distribution dependent stochastic differential equations driven by time-changed Brownian motion is studied. The existence and uniqueness theorem of strong solutions for the distribution dependent stochastic differential equations is established. Then, sufficient conditions...
| Published in: | Applied Mathematics and Optimization |
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| ISSN: | 0095-4616 1432-0606 |
| 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/cronfa62689 |
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| Abstract: |
In this paper, a class of distribution dependent stochastic differential equations driven by time-changed Brownian motion is studied. The existence and uniqueness theorem of strong solutions for the distribution dependent stochastic differential equations is established. Then, sufficient conditions are provided to guarantee the solutions to be stable in several different senses in terms of Lyapunov function. Finally, we show that the solutions of the distribution dependent stochastic differential equations can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence. |
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| Keywords: |
Distribution dependent stochastic differential equations;Time-changed Brownian motions; Stability; Averaging principle. |
| College: |
Faculty of Science and Engineering |
| Funders: |
National Natural Science Foundation of China - 12071003 |
| Issue: |
2 |