This research axis consists of two parts. The first part deals with large deviations properties of quadratic forms of Gaussian processes and Brownian diffusion. One can also cite recent work on large deviations of least squares estimators of the unknown parameters of Ornstein-Uhlenbeck process with shift. The second part is dedicated to concentration inequalities for sums of independent random variables and martingales. A book is forthcoming, with some applications of concentration inequalities in probabilities and statistics, particularly on the autoregressive process, random permutations and random matrix spectrum.