An invariance principle for fractional Brownian sheets

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. (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. (2011).