Lucio Galeati and Massimiliano Gubinelli
We show that generic Hölder continuous functions are $\rho$-irregular. The property of $\rho$-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 $\rho$-irregular and study in detail the geometric and analytic properties of $\rho$-irregular functions.
Lucio Galeati and Massimiliano Gubinelli. Prevalence of $\rho$-irregularity and related properties. Papers of Massimiliano Gubinelli, 2020, version 2. https://mgubi.org/papers/paper/rho-irregularity-prevalence/
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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.