Non-local SDEs, critical drifts and local blow-ups

Abstract

The paper is concerned with $\alpha$-stable SDEs with singular time-inhomogeneous general drift. Our drifts satisfy a condition that is close to the minimal possible scaling-invariance and can introduce local blow-ups of the type arising in some particle systems with strong attracting interactions.

Fixed a minor error in the proof of Proposition 3. Fixed a number of typos