Regularity and Sensitivity for McKean-Vlasov Type SPDEs Generated by Stable-like Processes

TL;DR

This paper investigates the sensitivity of McKean-Vlasov SPDEs driven by stable-like processes, using stochastic characteristics to relate them to non-stochastic equations, with applications to mean-field games with common noise.

Contribution

It introduces a novel approach using stochastic characteristics to analyze the sensitivity of McKean-Vlasov SPDEs driven by stable-like processes, extending previous PDE results.

Findings

Established a method to transfer McKean-Vlasov SPDEs to non-stochastic equations with random coefficients.

Provided insights into the sensitivity analysis relevant for mean-field games with common noise.

Extended the theoretical framework for nonlinear PDEs generated by stable-like processes.

Abstract

In this paper we study the sensitivity of nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes. By using the method of stochastic characteristics, we transfer these equations to the non-stochastic equations with random coefficients thus making it possible to use the results obtained for nonlinear PDE of McKean-Vlasov type generated by stable-like processes in the previous works. The motivation for studying sensitivity of nonlinear McKean-Vlasov SPDEs arises naturally from the analysis of the mean-field games with common noise.