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We show that generic Holder 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.
The paper is concerned with the properties of solutions to linear evolution equation perturbed by cylindrical Levy processes. It turns out that solutions, under rather weak requirements, do not have c`adl`ag modification. Some natural open questions are also stated.
A fundamental question in rough path theory is whether the expected signature of a geometric rough path completely determines the law of signature. One sufficient condition is that the expected signature has infinite radius of convergence, which is s
We improve the constant $frac{pi}{2}$ in $L^1$-Poincare inequality on Hamming cube. For Gaussian space the sharp constant in $L^1$ inequality is known, and it is $sqrt{frac{pi}{2}}$. For Hamming cube the sharp constant is not known, and $sqrt{frac{pi
We present two results characterizing minimizers of the Chan-Esedoglu L1TV functional $F(u) equiv int | abla u | dx + lambda int |u - f| dx $; $u,f:Bbb{R}^n to Bbb{R}$. If we restrict to $u = chi_{Sigma}$ and $f = chi_{Omega}$, $Sigma, Omega in Bbb{R
We derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by jump SDEs with adapted coefficients in weighted Holder norms using the Sobolev embedding theorem and the change of variable formula. As an appli