A central limit theorem for fields of martingale differences

Dalibor Volny

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arXiv · 1504.02439

A central limit theorem for fields of martingale differences

Dalibor Volny

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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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Dalibor Volny. 2015-04-09. A central limit theorem for fields of martingale differences. https://arxiv.org/abs/1504.02439

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