On limit theorems for fields of martingale differences

Dalibor Volný

Stochastic Processes and their Applications, 2019, vol. 129, issue 3, 841-859

Abstract: We prove a central limit theorem for stationary multiple (random) fields of martingale differences f∘Ti̲, i̲∈Zd, where Ti̲ is a Zd action. In most cases the multiple (random) fields of martingale differences is given by a completely commuting filtration. A central limit theorem proving convergence to a normal law has been known for Bernoulli random fields and in Volný (2015) this result was extended to random fields where one of generating transformations is ergodic.

Date: 2019
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DOI: 10.1016/j.spa.2018.03.021

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