The central limit theorem for a sequence of random processes with space varying long memory

Abstract

In this paper we investigate a sequence of square integrable random processes with space varying memory. We establish sufficient conditions for the central limit theorem in the space $L^2(\mu )$ for the partial sums of the sequence of random processes with space varying long memory. Of particular interest is a non-standard normalization of the partial sums in the central limit theorem.

11 pages, 1 figure

Cited by in corpus (3)

• Operator self-similar processes and functional central limit theorems
• Limit theorems for Hilbert space-valued linear processes under long range dependence
• Limit theorems for multivariate long-range dependent processes