Distribution Dependent SDEs with H\"{o}lder Continuous Drift and $\alpha$-Stable Noise

TL;DR

This paper investigates the existence, uniqueness, and numerical approximation of distribution-dependent SDEs with Hölder continuous drift driven by α-stable noise, extending results from classical SDEs.

Contribution

It establishes existence and uniqueness for distribution-dependent SDEs with Hölder continuous drift and analyzes the convergence rate of Euler-Maruyama method using Zvonkin transformation.

Findings

Proved existence and uniqueness of solutions.

Derived convergence rate of Euler-Maruyama method.

Extended classical SDE results to distribution-dependent case.

Abstract

In this paper, the existence and uniqueness of the distribution dependent SDEs with H\"{o}lder continuous drift driven by $\alpha$-stable process is investigated. Moreover, by using Zvonkin type transformation, the convergence rate of Euler-Maruyama method is also obtained. The results cover the ones in the case of distribution independent SDEs.