Propagation of chaos for stochastic particle systems with singular mean-field interaction of $L^q-L^p$ type

TL;DR

This paper establishes the well-posedness and propagation of chaos for stochastic particle systems with singular mean-field interactions characterized by $L^q-L^p$ spaces, using novel partial Girsanov transformations.

Contribution

It introduces a new approach employing partial Girsanov transformations to prove well-posedness and chaos propagation for systems with singular kernels in $L^q-L^p$ spaces.

Findings

Proves well-posedness of the particle system

Establishes propagation of chaos under $L^q-L^p$ conditions

Develops a new method using partial Girsanov transformations

Abstract

In this work, we prove the well-posedness and propagation of chaos for a stochastic particle system in mean-field interaction under the assumption that the interacting kernel belongs to a suitable $L_t^q-L_x^p$ space. Contrary to the large deviation principle approach recently proposed in [2], the main ingredient of the proof here are the \textit{Partial Girsanov transformations} introduced in [3] and developed in a general setting in this work.