Nonlinear Young integrals have been first introduced in Catellier and Gubinelli (Stoch
Process Appl 126 (8): 2323–2366, 2016) and provide a natural generalisation of classical …

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 …

We investigate the regularizing effect of certain additive continuous perturbations on SDEs
with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on …

We study a rough difference equation on a discrete time set, where the driving Hölder rough
path is a realization of a stochastic process. Using a modification of Davie's approach (Cong …

In this paper we prove that under mild conditions a nonautonomous Young differential
equation possesses a unique solution which depends continuously on initial conditions. The …

This paper deals with the consistency and a rate of convergence for a Nadaraya–Watson
estimator of the drift function of a stochastic differential equation driven by an additive …

Rough differential equations are solved for signals in general Besov spaces unifying in
particular the known results in Hölder and p-variation topology. To this end the …

We provide a unified analytic approach to study the asymptotic dynamics of Young
differential equations, using the framework of random dynamical systems and random …

The Itô map gives the solution of a Rough Differential Equation, a generalization of an
Ordinary Differential Equation driven by an irregular path, when existence and uniqueness …

This thesis concerns the study of regularisation by noise phenomena for ODEs and PDEs. In
particular, it focuses on the use of so called pathwise techniques: our aim is to identify …