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

Tae-Sung Kim

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



DOI: http://dx.doi.org/10.21914/anziamj.v49i0.96



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.