Abstract : The study of the p-variation of a process in probability is not new. It is indeed initiated by authors including, for example Levy (1940), Blumenthal and Getoor (1960, 1961), Monroe (1972), Bretagnolle (1972) and Lépingle (1976).
It was a craze in recent years in relation to their proven usefulness in the estimation of volatility and testing for the presence of jumps in financial mathematics.
In this thesis, we generalize some results in this area with random functions which depend also on time and space.
We prove the convergence of these processes and under certain conditions, we give the central limit theorem associated.
The most applications of our are on statistical process, about the convergence of the functions of contrasts.