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arXiv:2004.00872math.PR

Prevalence of $ρ$-irregularity and related properties

Lucio Galeati, Massimiliano Gubinelli

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Abstract

We show that generic Hölder continuous functions are $ρ$-irregular. The property of $ρ$-irregularity has been first introduced by Catellier and Gubinelli (Stoc. Proc. Appl. 126, 2016) and plays a key role in the study of well-posedness for some classes of perturbed ODEs and PDEs. Genericity here is understood in the sense of prevalence. As a consequence we obtain several results on regularisation by noise "without probability", i.e. without committing to specific assumptions on the statistical properties of the perturbations. We also establish useful criteria for stochastic processes to be $ρ$-irregular and study in detail the geometric and analytic properties of $ρ$-irregular functions.

arXiv comments
Final accepted version
Journal reference
DOI
Subjects
math.PRProbability math.APAnalysis of PDEs math.CAClassical Analysis and ODEs

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  1. TeXmacs and the Art of Mathematical Writing 1 comment

    • 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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