Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations
Abstract
In this paper, we consider the averaging principle for a class of McKean-Vlasov stochastic differential equations with slow and fast time-scales. Under some proper assumptions on the coefficients, we first prove that the slow component strongly converges to the solution of the corresponding averaged equation with convergence order $1/3$ using the approach of time discretization. Furthermore, under stronger regularity conditions on the coefficients, we use the technique of Poisson equation to improve the order to $1/2$, which is the optimal order of strong convergence in general.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2019
- DOI:
- 10.48550/arXiv.1909.07665
- arXiv:
- arXiv:1909.07665
- Bibcode:
- 2019arXiv190907665R
- Keywords:
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- Mathematics - Probability
- E-Print:
- 33 pages. We revised some typos and added some references in the previous version