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

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 $(1-\alpha )$-Hölder semi-norm of $b$ is sufficient small.

References in corpus (4)

• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
• Viscosity methods giving uniqueness for martingale problems
• Well-posedness of supercritical SDE driven by Lévy processes with irregular drifts
• Hôlder continuity of solutions of second-order non-linear elliptic integro-differential equations