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Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations
- Publication Year :
- 2019
-
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.<br />Comment: 33 pages. We revised some typos and added some references in the previous version
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1909.07665
- Document Type :
- Working Paper