A note on asymptotic expansions for Markov chains using operator theory
type: Item
instance of: scholarly article
title: A note on asymptotic expansions for Markov chains using operator theory
zbMATH Open document ID: 0635.60024
DOI: 10.1016/0196-8858(87)90016-9
published in: Advances in Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The author shows that the result of \textit{S. V. Nagaev} [Teor. Veroyatn. Primen 2, 389-416 (1958; Zbl 0078.318); English translation in Theory Probab. Appl. 2, 378-406 (1957)] on the decomposition of the characteristic function of a sum of random variables connected in a Markov chain can be proved under much weaker conditions. In particular he relaxes the conditional moment and ergodicity conditions (requiring exponentially fast convergence of the shift operator in \(L^ p\)-strong operator topology) to derive Nagaev's eigenvalue decomposition which might be used to derive expansion results for sums of Markov chain variables.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 4034752
zbMATH Keywords: decomposition of the characteristic function of a sum of random variables
zbMATH Keywords: conditional moment and ergodicity conditions
zbMATH Keywords: exponentially fast convergence of the shift operator
zbMATH Keywords: eigenvalue decomposition
author: Jens Ledet Jensen
reviewed by: Friedrich Götze
MaRDI profile type: Publication
full work available at URL: 0196-8858(87)90016-9
OpenAlex ID: W2004338565
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description: scientific article; zbMATH DE number 4034752