Weak solution for distribution dependent SDEs driven by L\'{e}vy noise

TL;DR

This paper proves the existence of weak solutions for distribution-dependent SDEs driven by Lévy noise, using Krylov estimates and tightness arguments under certain conditions.

Contribution

It introduces a method to establish weak solutions for DDSDEs with Lévy noise, expanding the understanding of such stochastic systems.

Findings

Existence of weak solutions under broad Lévy noise conditions

Application of Krylov-type estimates to DDSDEs

Use of tightness arguments to prove solution existence

Abstract

In this paper, we establish the existence of weak solutions for distribution-dependent stochastic differential equations (DDSDEs) driven by a broad class of L\'{e}vy noises, where the drift coefficients satisfy specific integrability conditions. This is achieved through the Krylov-type estimate and tightness argument.