The central limit theorem for a sequence of random processes with space-varying long memory* |
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Authors: | Vaidotas Characiejus Alfredas Račkauskas |
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Institution: | 1. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania
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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(μ) for the partial sums of the sequence of random processes with space-varying long memory. Of particular interest is a nonstandard normalization of the partial sums in the central limit theorem. |
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