arXiv:2003.14264math.CA
Noiseless regularisation by noise
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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".
I generally use TeXmacs for notes, derivations, lectures, articles, all, of course. Most of my papers in the last 7 years, around 15 and all my lectures in the same period, circa 2 courses a year. More in detail, all these papers are been written completely in TeXmacs and then…
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