Optimality properties for the estimation of jumps in stochastic processes

Statistics and Modeling for Complex Data

In this paper, we study the problem of optimal estimation of the size of jumps for diffusion processes.
We prove some LAMN property in the case where the instants of jumps are random and the size of jumps are deterministic.
We study too the situation where both the instants and sizes of jumps are random, and prove some Hajek's convolution theorem in this case.

This is a joint work with E. Clément (Université Paris Est) and Sylvain Delattre (Université Paris 7)