G\"artner-Ellis condition for squared asymptotically stationary Gaussian processes
Probability
2015-02-17 v1
Abstract
The G\"artner-Ellis condition for the square of an asymptotically stationary Gaussian process is established. The same limit holds for the conditional distri-bution given any fixed initial point, which entails weak multiplicative ergodicity. The limit is shown to be the Laplace transform of a convolution of Gamma distributions with Poisson compound of exponentials. A proof based on Wiener-Hopf factorization induces a probabilistic interpretation of the limit in terms of a regression problem.
Cite
@article{arxiv.1502.04218,
title = {G\"artner-Ellis condition for squared asymptotically stationary Gaussian processes},
author = {Marina Kleptsyna and Alain Le Breton and Bernard Ycart},
journal= {arXiv preprint arXiv:1502.04218},
year = {2015}
}