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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