An invariance principle for stationary random fields under Hannan’s condition

Dalibor Volný and Yizao Wang

Stochastic Processes and their Applications, 2014, vol. 124, issue 12, 4012-4029

Abstract: We establish an invariance principle for a general class of stationary random fields indexed by Zd, under Hannan’s condition generalized to Zd. To do so we first establish a uniform integrability result for stationary orthomartingales, and second we establish a coboundary decomposition for certain stationary random fields. At last, we obtain an invariance principle by developing an orthomartingale approximation. Our invariance principle improves known results in the literature, and particularly we require only finite second moment.

Keywords: Invariance principle; Brownian sheet; Random field; Orthomartingale; Hannan’s condition; Weak dependence (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (10)

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DOI: 10.1016/j.spa.2014.07.015

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