Ivanenko D. Asymptotic properties of parameters estimators of Markov processes with Poisson noises

A comprehensive method is developed, which applies well to the study of asymptotic properties of unknown parameters estimators in statistical systems generated by discrete observations of the solution to SDE with Levy noises without the diffusion component. This method is based on an appropri- ate modification of the Malliavin calculus, and is used in the thesis to prove the LAN property for two types of statistical models: a nonlinear one with light tails of the noise, and a linear one with high frequency of observation and possibly heavy tails of the noise.