Lucio Galeati and Massimiliano Gubinelli
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".
Lucio Galeati and Massimiliano Gubinelli. Noiseless regularisation by noise. Papers of Massimiliano Gubinelli, 2020, version 2. https://mgubi.org/papers/paper/noiseless-regularisation/
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Papers of Massimiliano Gubinelli: an OpenSheaf archive (format 0.1, a draft); this page is generated by opensheaf-py from the archive.