On the quenched CLT for stationary random fields under projective criteria
Probability
2019-09-12 v3
Abstract
Motivated by random evolutions which do not start from equilibrium, in a recent work, Peligrad and Voln\'{y} (2018) showed that the quenched CLT (central limit theorem) holds for ortho-martingale random fields. In this paper, we study the quenched CLT for a class of random fields larger than the ortho-martingales. To get the results, we impose sufficient conditions in terms of projective criteria under which the partial sums of a stationary random field admit an ortho-martingale approximation. More precisely, the sufficient conditions are of the Hannan's projective type. As applications, we establish quenched CLT's for linear and nonlinear random fields with independent innovations.
Keywords
Cite
@article{arxiv.1809.08686,
title = {On the quenched CLT for stationary random fields under projective criteria},
author = {Na Zhang and Lucas Reding and Magda Peligrad},
journal= {arXiv preprint arXiv:1809.08686},
year = {2019}
}