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

Röckner, Michael; Sun, Xiaobin; Xie, Yingchao

doi:10.1214/20-aihp1087

Cited by 45 publications

(39 citation statements)

References 33 publications

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“…We first investigate the central limit type theorem for slow-fast McKean-Vlasov stochastic system (1.2). The following result for the existence and uniqueness of strong solutions to (1.2) has been proved in the recent work [54].…”

Section: Central Limit Type Theoremmentioning

confidence: 98%

“…(iv) Here we present a simple example of distribution dependent coefficient such that A2 holds, which follows from [41,Example 2.16] (see also [54,Example 5.1]).…”

Section: Main Frameworkmentioning

confidence: 99%

“…Moreover, the authors in [54] have proved the following convergence rate of the averaging principle for stochastic system (1.2), sup…”

Section: Central Limit Type Theoremmentioning

confidence: 99%

“…Under the conditions A1 and A2, by a straightforward computation (see [54,Proposition 4.1]), we can see that sup…”

Section: Regularity Of the Solution Of Poisson Equationmentioning

confidence: 99%

“…Therefore, a simplified equation which governs the evolution of the system over a long time scale would be highly desirable and useful for applications. Under certain assumptions, Röckner et al [54] proved that the slow component X ε t in system (1.2) will converge strongly to the solution of the so-called averaged equation, i.e. sup t∈[0,T ]…”

Section: Introductionmentioning

confidence: 99%

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Central Limit Type Theorem and Large Deviations for Multi-Scale McKean-Vlasov SDEs

Wang¹,

Li²,

Liu³

et al. 2021

Preprint

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In this paper, we aim to study the asymptotic behavior for multiscale McKean-Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e, the deviation between the slow component X ε and the solution X of the averaged equation converges weakly to a limiting process. More precisely,to the solution of certain distribution dependent stochastic differential equation, which involves an extra explicit stochastic integral term. Secondly, in order to estimate the probability of deviations away from the limiting process, we further investigate the Freidlin-Wentzell's large deviation principle for multi-scale McKean-Vlasov stochastic system. The main techniques are based on the Poisson equation for central limit type theorem and the weak convergence approach for large deviation principle. To the best of our knowledge, this is the first central limit type theorem and large deviations result established for multi-scale McKean-Vlasov stochastic systems.

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Section: Central Limit Type Theoremmentioning

confidence: 98%

“…(iv) Here we present a simple example of distribution dependent coefficient such that A2 holds, which follows from [41,Example 2.16] (see also [54,Example 5.1]).…”

Section: Main Frameworkmentioning

confidence: 99%

“…Moreover, the authors in [54] have proved the following convergence rate of the averaging principle for stochastic system (1.2), sup…”

Section: Central Limit Type Theoremmentioning

confidence: 99%

“…Under the conditions A1 and A2, by a straightforward computation (see [54,Proposition 4.1]), we can see that sup…”

Section: Regularity Of the Solution Of Poisson Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Central Limit Type Theorem and Large Deviations for Multi-Scale McKean-Vlasov SDEs

Wang¹,

Li²,

Liu³

et al. 2021

Preprint

Self Cite

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show abstract

Large deviation principle for multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motions

Shen,

Zhou,

2024

J. Evol. Equ.

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On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions

Shen,

Zhang,

Song

et al. 2023

Appl Math Optim

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

Cited by 45 publications

References 33 publications

Central Limit Type Theorem and Large Deviations for Multi-Scale McKean-Vlasov SDEs

Central Limit Type Theorem and Large Deviations for Multi-Scale McKean-Vlasov SDEs

Large deviation principle for multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motions

On a Class of Distribution Dependent Stochastic Differential Equations Driven by Time-Changed Brownian Motions

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