In the first part of the talk, I give a Varadhan estimates for big order differential operators by mixing Wentzel-Freidlin estimates and the Malliavin Calculus of BIsmut type in an intrinsic way I have constructed recently.

In the second part, I give an approach to the Wong-Zakai approximation for semi-groups generated by big order differential generators.

In the last part, I establish for big order generators a generalization of the classical flow theorem of Malliavin for diffusions.

Rémi Léandre, directeur de recherches in CNRS at the University of Franche-Comté, has written about 170 papers about the applications of the Malliavin Calculus, the Hida Calculus and the stochastic differential geometry to analysis, geometry and mathematical physics. He received Bronze Medal of C.N.R.S.in 1988  and Rollo Davidson Prize in 1989 for some works on hypoelliptic diffusions. He has organized several conferences in France and published two books in honour of J.M. Bismut in Astérisque (French Mathematical Society) in 2009 with X. Dai, X. Ma and W. Zhang.