Strong convergence order for slow–fast McKean–Vlasov stochastic differential equations

By Michael Röckner, Xiaobin Sun, Yingchao Xie. Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2019

80 citations recorded by the source corpus.

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.

Subfields: Demography, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/26ae37cb91729223288afdd9ef1407732d4b66b3

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In Demography

1. Wei Hong
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In Finance

1. Wei Hong
2. Shihu Li
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In Modeling and Simulation

1. Wei Hong
2. Shihu Li
3. Wei Liu

Citations in the corpus

• Strong convergence rates in averaging principle for slow-fast McKean-Vlasov SPDEs (2021, methodology): “We need to point out that compared with the results of McKean-Vlasov SDEs in [42], in order to cover some infinite dimensional nonlinear SPDE models, we now consider the system in two Gelfand triples, thus we have to derive some apriori estimates of solutions involving different spaces and overcome ”