Regularisation by regular noise

Abstract

We show that perturbing ill-posed differential equations with (potentially very) smooth random processes can restore well-posedness -- even if the perturbation is (potentially much) more regular than the drift component of the solution. The noise considered is of fractional Brownian type, and the familiar regularity condition $\alpha >1-1/(2H)$ is recovered for all non-integer $H>1$.

13 pages

References in corpus (2)

• Multidimensional SDE with distributional drift and Lévy noise
• Singular paths spaces and applications

Cited by in corpus (3)

• Pathwise Regularisation of Singular Interacting Particle Systems and their Mean Field Limits
• Weak well-posedness for degenerate SDEs driven by Lévy processes
• Stochastic sewing in Banach space