# Fabian Andsem Harang

**Abstract**

The theory of regularization by noise is concerned with discovering the regularizing effects that stochastic or deterministic noise may have on ordinary and partial differential equations. In this presentation I will give a short review of recent results in this theory, as well as some applications.

In particular, I will begin to show a simple strategy to prove the regularizing effect of differential equations using the concept of averaging operators given as deterministic Riemann integral of a function along an irregular path. A specific example of such averaging operator can be obtained from the local time of a stochastic processes. Using these operators we construct a solution theory for equations driven by a non-linear Young integral. I will then show some applications of these techniques towards the regularization of ill-posed and singular ODEs and PDEs perturbed by noise.