A central limit theorem for fields of martingale differences

2015/04/09 by Dalibor Volny, Volny, Dalibor
Mathematics · #28D05 #60F05 #60G42 #60G60 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:28D05 #msc:60F05 #msc:60G42 #msc:60G60

paper · pdf · doi:10.48550/arxiv.1504.02439

arxiv created 2015/04/09 · arxiv updated 2015/04/10

Abstract

We prove a central limit theorem for a random field generated by d commuting probability preserving transformations; the martingale is given by a commuting filtration (cf. D. Khosnevisan, Multiparameter Processes, Springer 2002). The result has been known for Bernoulli random fields. Here, only ergodicity of one of generating transformations is supposed.

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