Limit theorems for weighted Bernoulli random fields under Hannan’s condition

Jana Klicnarová, Dalibor Volný and Yizao Wang

Stochastic Processes and their Applications, 2016, vol. 126, issue 6, 1819-1838

Abstract: Recently, invariance principles for partial sums of Bernoulli random fields over rectangular index sets have been proved under Hannan’s condition. In this note we complement previous results by establishing limit theorems for weighted Bernoulli random fields, including central limit theorems for partial sums over arbitrary index sets and invariance principles for Gaussian random fields. Most results improve earlier ones on Bernoulli random fields under Wu’s condition, which is stronger than Hannan’s condition.

Keywords: Invariance principle; Hannan’s condition; Stationary random field; m-dependent approximation (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2015.12.006

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