Well-posedness and averaging principle of McKean-Vlasov SPDEs driven by cylindrical $\alpha$-stable process

TL;DR

This paper establishes the well-posedness and averaging principle for McKean-Vlasov SPDEs driven by cylindrical alpha-stable processes, providing a rigorous foundation and convergence rate for multiscale stochastic systems.

Contribution

It proves well-posedness and the averaging principle for a class of McKean-Vlasov SPDEs driven by cylindrical alpha-stable processes, with explicit convergence rates.

Findings

Proved well-posedness of McKean-Vlasov SPDEs with cylindrical alpha-stable noise.

Established averaging principle with strong convergence rate.

Demonstrated applicability to multiscale stochastic systems.

Abstract

In this paper, we first study the well-posedness of a class of McKean-Vlasov stochastic partial differential equations driven by cylindrical $\alpha$-stable process, where $\alpha\in(1,2)$. Then by the method of the Khasminskii's time discretization, we prove the averaging principle of a class of multiscale McKean-Vlasov stochastic partial differential equations driven by cylindrical $\alpha$-stable processes. Meanwhile, we obtain a specific strong convergence rate.