Strong convergence rates in averaging principle for slow-fast McKean-Vlasov SPDEs

Hong, Wei; Li, Shihu; Liu, Wei

doi:10.1016/j.jde.2022.01.039

Cited by 28 publications

(6 citation statements)

References 36 publications

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“…Then by a standard argument (cf. [47] or [31]), it is straightforward that X = X, dt × P-a.e.. Therefore, due to [47, Theorem 4.2.5], X is an H-valued continuous (F t )-adapted process, moreover, we can get the following energy estimates…”

Section: Existence Of Variational Solutionsmentioning

confidence: 96%

McKean-Vlasov SDEs and SPDEs with Locally Monotone Coefficients

Wang¹,

Hu²,

Liu³

2022

Preprint

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In this paper we mainly investigate the strong and weak wellposedness of a class of McKean-Vlasov stochastic (partial) differential equations. The main existence and uniqueness results state that we only need to impose some local assumptions on the coefficients, i.e. locally monotone condition both in state variable and distribution variable, which cause some essential difficulty since the coefficients of McKean-Vlasov stochastic equations typically are nonlocal. Furthermore, the large deviation principle is also derived for the McKean-Vlasov stochastic equations under those weak assumptions. The wide applications of main results are illustrated by various concrete examples such as the Granular media equations, Kinetic equations, distribution dependent porous media equations and Navier-Stokes equations, moreover, we could remove or relax some typical assumptions previously imposed on those models.

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Section: Existence Of Variational Solutionsmentioning

confidence: 96%

McKean-Vlasov SDEs and SPDEs with Locally Monotone Coefficients

Wang¹,

Hu²,

Liu³

2022

Preprint

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“…[7,10,14,18,22,34,39] and reference therein for the classical SDEs or SPDEs (i.e. distribution independent case) and to [19,37,44] for the case of distribution dependence.…”

Section: Introductionmentioning

confidence: 99%

Diffusion Approximation for Multi-Scale McKean-Vlasov SDEs Through Different Methods

Wang¹,

Li²,

Sun³

2022

Preprint

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In this paper, we aim to study the diffusion approximation for multi-scale McKean-Vlasov stochastic differential equations. More precisely, we prove the weak convergence of slow process X ε in C([0, T ]; R n ) towards the limiting process X that is the solution of a distribution dependent stochastic differential equation in which some new drift and diffusion terms compared to the original equation appear. The main contribution is to use two different methods to explicitly characterize the limiting equations respectively. The obtained diffusion coefficients in the limiting equations have different form through these two methods, however it will be asserted that they are essential the same by a comparison.

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“…Recall that the strong convergence rate of averaging principle for slow-fast Mckean-Vlasov SDE was established by the techniques of time discretization and Poisson equation in [36]. And as discussed in [22], the strong convergence rate of averaging principle for slow-fast Mckean-Vlasov SPDE was studied based on the variational approach and the technique of time discretization. Note that the coefficients of the slow equation with fast variables were global Lipschitz continuous with respect to slow variable in the above results.…”

Section: Introductionmentioning

confidence: 99%

“…Example 1.7 below), which is the same rate in [36] when δ = 0. Moreover, the rate in [22] is ε 1 6 .…”

Section: Introductionmentioning

confidence: 99%

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Strong and weak convergence for averaging principle of DDSDE with singular drift

Cheng¹,

Hao²,

Röckner³

2022

Preprint

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In this paper, we study averaging principle for distribution dependent stochastic differential equations with localized L p drift. Using Zvonkin's transformation and estimates for Kolmogorov equations, we prove that the solution of the original system strongly and weakly converges to the solution of averaged system as the time scale ε goes to zero. Moreover, we show the rates of strong and weak convergence depend on the singularity of the drift respectively.

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Strong convergence rates in averaging principle for slow-fast McKean-Vlasov SPDEs

Cited by 28 publications

References 36 publications

McKean-Vlasov SDEs and SPDEs with Locally Monotone Coefficients

McKean-Vlasov SDEs and SPDEs with Locally Monotone Coefficients

Diffusion Approximation for Multi-Scale McKean-Vlasov SDEs Through Different Methods

Strong and weak convergence for averaging principle of DDSDE with singular drift

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