Martingale-coboundary decomposition for stationary random fields

Abstract

We prove a martingale-coboundary representation for random fields with a completely commuting filtration. For random variables in L2 we present a necessary and sufficient condition which is a generalization of Heyde's condition for one dimensional processes from 1975. For Lp spaces with 2 \leq p < \infty we give a necessary and sufficient condition which extends Volny's result from 1993 to random fields and improves condition of El Machkouri and Giraudo from 2016 (arXiv:1410.3062). In application, new weak invariance principle and estimates of large deviations are found.

Stochastics and Dynamics 2017

References in corpus (2)

• Comparison between criteria leading to the weak invariance principle
• Martingale approximation of non-stationary stochastic processes

Cited by in corpus (1)

• Martingale approximations for random fields