Stochastic Analysis is the analytical study of phenomena with a random component. It is based on works of Wiener, Itô, Cameron-Martin, Girsanov and others, and can be also interpreted as the mathematical framework underlying Feynman path integral approach to Quantum Physics. Traditionally we have been using Malliavin calculus of variations, a theory of differentiation on the path space equipped with the Wiener measure, which is adapted to very irregular functionals like the ones generated by Itô calculus.

Recently a large part of our activity in this area is devoted to Stochastic Geometric Mechanics.