À l'ENSTA Paris - 15h00

Title : Stochastic analysis of non-Markovian irregular phenomena.

This thesis focuses on some particular stochastic analysis aspects of non-Markovian irregular phenomena. It formulates existence and uniqueness for some martingale problems involving two types of irregular drifts perturbed by path-dependent functionals: the first one is related to the case which is the derivative of continuous function and it models irregular path-dependent media; the second one concerns the case when the drift is of Bessel type in low dimension. Finally the thesis also focuses on rough paths techniques and its relation with the stochastic calculus via regularization.