Title

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

Article Type

Research Article

Publication Title

Annals of Probability

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.

First Page

178

Last Page

210

DOI

10.1214/19-AOP1358

Publication Date

1-1-2020

Comments

Open Access, Green

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