Strong existence and uniqueness for stable stochastic differential equations with distributional drift

Abstract

We consider the stochastic differential equation dXt b(Xt +dLt, where the drift b is a generalized function and L is a symmetric one dimensional α-stable Levy processes, α ∈ (1, 2). We define the notion of solution to this equation and establish strong existence and uniqueness whenever b belongs to the Besov-Holder space Cβ for β >1/2-α/2.