Noiseless regularisation by noise
Classical Analysis and ODEs
2020-12-15 v2 Analysis of PDEs
Probability
Abstract
We analyse the effect of a generic continuous additive perturbation to the well-posedness of ordinary differential equations. Genericity here is understood in the sense of prevalence. This allows us to discuss these problems in a setting where we do not have to commit ourselves to any restrictive assumption on the statistical properties of the perturbation. The main result is that a generic continuous perturbation renders the Cauchy problem well-posed for arbitrarily irregular vector fields. Therefore we establish regularisation by noise "without probability".
Cite
@article{arxiv.2003.14264,
title = {Noiseless regularisation by noise},
author = {Lucio Galeati and Massimiliano Gubinelli},
journal= {arXiv preprint arXiv:2003.14264},
year = {2020}
}
Comments
Remark 21 and Section 5.2 revisited; Remark 11 added; typos corrected, references added