Strong Existence and Uniqueness for Singular SDEs Driven by Stable Processes
- Authors: Leonid Mytnik, Johanna Weinberger
- First public date: 2024-04-21
- arXiv: 2404.13729
- Preprint year: 2024
- Status: Published
- Publication type: Journal article
- Publication year: 2026
- Journal: Annals of Applied Probability 36(2), 1690–1736 (2026)
- DOI: 10.1214/25-AAP2267
Abstract
We consider one-dimensional stochastic differential equations driven by a symmetric stable process with a finite measure-valued drift in a Kato class. We prove weak and strong well-posedness in the sharp parameter ranges, reformulate the equation using the solution’s local time, and derive a Tanaka-type formula for stable processes perturbed by adapted finite-variation processes.