On functional central limit theorems for linear random fields with dependent innovtions

Abstract

For a linear random field (linear p-parameter stochastic process) generated by a dependent random field with zero mean and finite qth moments (q>2p), we give sufficient conditions that the linear random field converges weakly to a multiparameter standard Brownian motion if the corresponding dependent random field does so. doi:10.1017/S1446181108000217