Bias correction for drift and volatility estimation of jump diffusion processes and non - parametric adaptive estimation of the invariant measure.

Summary The subject of the thesis is parametric and non-parametric estimation in jump process models. The thesis is composed of 3 parts which regroup 4 works. The first part, which is composed of two chapters, deals with the estimation of drift and volatility parameters by contrast methods from discrete observations, with the main objective of minimizing the conditions on the observation step, so that it can for example go arbitrarily slowly towards 0. The second part of the thesis concerns asymptotic developments, and bias correction, for the estimation of the integrated volatility. The third part of the thesis, concerns the adaptive estimation of the stationary measure for jump processes.