An Invariance Principle for Fractional Brownian Sheets

Yizao Wang ()
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Yizao Wang: University of Cincinnati

Journal of Theoretical Probability, 2014, vol. 27, issue 4, 1124-1139

Abstract: Abstract We establish a central limit theorem for partial sums of stationary linear random fields with dependent innovations, and an invariance principle for anisotropic fractional Brownian sheets. Our result is a generalization of the invariance principle for fractional Brownian motions by Dedecker et al. (Bernoulli 17:88–113, 2011) to high dimensions. A key ingredient of their argument, the martingale approximation, is replaced by an $$m$$ -approximation argument. An important tool of our approach is a moment inequality for stationary random fields recently established by El Machkouri et al. (Stoch. Process. Appl. 123:1–14, 2013).

Keywords: $$m$$ -Dependence; Central limit theorem; Invariance principle; Fractional Brownian sheet; 60F17; 60G22 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-013-0483-2

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