Weak uniqueness for SDEs driven by supercritical stable processes with Holder drifts

TL;DR

This paper proves weak uniqueness for certain supercritical stable process-driven SDEs with Holder continuous drifts, establishing well-posedness under smallness conditions on the drift's semi-norm.

Contribution

It demonstrates weak well-posedness of SDEs driven by supercritical stable processes with Holder drifts, a novel result in the context of such stochastic systems.

Findings

Weak well-posedness established for supercritical stable process-driven SDEs

Weak uniqueness holds when the drift's Holder semi-norm is sufficiently small

Applicable to rotational symmetric alpha-stable processes

Abstract

In this paper, we investigate stochastic differential equations(SDEs) driven by a class of supercritical $\alpha$-stable process(including the rotational symmetric $\alpha-$stable process) with drift $b$. The weak well-posedness is proved, provided that the $(1-\alpha)$-H\"older semi-norm of $b$ is sufficient small.