A central limit theorem for stationary random fields

Mohamed El Machkouri, Dalibor Volný and Wei Biao Wu

Stochastic Processes and their Applications, 2013, vol. 123, issue 1, 1-14

Abstract: This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form Xk=g(εk−s,s∈Zd), k∈Zd, where (εi)i∈Zd are iid random variables and g is a measurable function. Such kind of spatial processes provides a general framework for stationary ergodic random fields. Under a short-range dependence condition, we show that the central limit theorem holds without any assumption on the underlying domain on which the process is observed. A limit theorem for the sample auto-covariance function is also established.

Keywords: Central limit theorem; Spatial processes; m-dependent random fields; Weak mixing (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (24)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:1:p:1-14

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DOI: 10.1016/j.spa.2012.08.014

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