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

By Wei Hong, Shihu Li, Wei Liu. Journal of Differential Equations, 2021

62 citations recorded by the source corpus.

In this paper, we aim to study the asymptotic behaviour for a class of McKean-Vlasov stochastic partial differential equations with slow and fast time-scales. Using the variational approach and classical Khasminskii time discretization, we show that the slow component strongly converges to the solution of the associated averaged equation. In particular, the corresponding convergence rates are also obtained. The main results can be applied to demonstrate the averaging principle for various McKean-Vlasov nonlinear SPDEs such as stochastic porous media type equation, stochastic p-Laplace type equation and also some McKean-Vlasov stochastic differential equations.

Subfields: Computational Mechanics, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/4637e2e1ae178562571cdc9d9a7c7a557b9dc64e

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In Computational Mechanics

1. Tusheng Zhang
2. Shijie Shang
3. Michael Röckner

In Finance

1. Tusheng Zhang
2. Shijie Shang
3. Michael Röckner
4. Wei Liu
5. Xicheng Zhang
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8. Giuseppe Da Prato

In Modeling and Simulation

1. Tusheng Zhang
2. Shijie Shang
3. Michael Röckner

Citations in the corpus

• Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, methodology): “see [48, 27, 5] for regularity of solutions, [18, 74, 47, 19, 88, 52, 61, 87, 37, 38] for large deviation principle, [31, 32, 33, 78, 65, 4, 90] for numerical approximation, [84, 46, 85, 86] for the Harnack inequality, gradient estimates, invariant measure and ergodicity, [28, 29] for random attract”