Local Asymptotic Normality for Linear Homogeneous Difference Equations with Non-Gaussian Noise

This paper considers the problem of estimation of drift parameter for linear homogeneous stochastic difference equations. The Local Asymptotic Normality (LAN) for the problem is proved. LAN implies the Hajek–Le Cam minimax lower bound. In particular, it is shown that the Fisher's information matrix for the problem can be expressed in terms of the stationary distribution of an auxiliary Markov chain on the projective space P(^d).