This document is a synthesis of my research activity since my PhD. The contributions are organized in three different parts. The first and second parts are dedicated to the statistical inference of stochastic processes. The main processes we study are the fractional Brownian motion (and some of its extensions) and spatial Gibbs point processes. These processes are of different nature but both are used to model data with strong (temporal or spatial) dependence. My contributions have for common points the study of asymptotic properties of estimation and validation methods. Another common point is the perspective to use these processes in applications dealing with complex systems in particular the modelling of signals derived from Functional Magnetic Resonance Imaging and the modelling of sunspots. Finally, the third part of this document gathers some works under the name contributions to applied statistics.
