Noiseless regularisation by noise

We analyse the effect of a $generic$ continuous additive perturbation to well-posedness ordinary differential equations. Genericity here is understood in sense prevalence. This allows us discuss these problems setting where we do not have commit ourselves any restrictive assumption on statistical properties perturbation. The main result that generic renders Cauchy problem well-posed for arbitrarily irregular vector fields. Therefore establish regularisation by noise “without probability”.