2017/06/24 by Dalibor Volny, Volny, Dalibor
Mathematics · #60F17 #60G42 #60G60 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F17 #msc:60G42 #msc:60G60
paper · pdf · doi:10.48550/arxiv.1706.07978
Stochastics and Dynamics 2017
arxiv created 2017/06/24 · arxiv updated 2017/06/27
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 ≤ p < ∞ 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.