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

Authors

Siva Athreya, Indian Statistical Institute, Kolkata
Oleg Butkovsky, Weierstrass Institutex
Leonid Mytnik, Technion - Israel Institute of Technology

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

Recommended Citation

Athreya, Siva; Butkovsky, Oleg; and Mytnik, Leonid, "Strong existence and uniqueness for stable stochastic differential equations with distributional drift" (2020). Journal Articles. 500.
https://digitalcommons.isical.ac.in/journal-articles/500