Noiseless regularisation by noise

Lucio Galeati; Massimiliano Gubinelli

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arXiv · 2003.14264

Noiseless regularisation by noise

Lucio Galeati·Massimiliano Gubinelli

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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".

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Lucio Galeati, Massimiliano Gubinelli. 2020-03-31. Noiseless regularisation by noise. https://arxiv.org/abs/2003.14264

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