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Contributions to the study of lévy processes and fractional processes via the Malliavin calculus and applications in statistics.

In the first part, we establish Itô’s and Tanaka’s formulas for the multidimensional bifractional Brownian motion. We study the existence of an occupation density for certain processes related to fractional Brownian motion. In the second part, we study the cubic variation of Rosenblatt process. We consider the problem of efficient estimation for the drift of fractional Brownian motion . We also construct superefficient James-Stein type estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator. In the last part, we study Skorohod integral processes on Lévy spaces and we prove an equivalence between this class of processes and the class of Itô-Skorohod process. We give a link between stable proceses and selfsimilaire processes through stochastic processes which are infinitely divisible with respect to time .