We translate in semi-group theory our proof of Varadhan estimates for subelliptic Laplacians which was using the theory of large deviations of Wentzel-Freidlin and the Malliavin Calculus of Bismut type. Key–Words: Large deviations. Subelliptic estimates.

Using the Malliavin calculus with respect to Gaussian processes and the multiple stochastic integrals we derive Itô’s and Tanaka’s formulas for the d-dimensional bifractional Brownian motion. 2000 AMS Classification Numbers: 60G12, 60G15, 60H05, 60H07.