On the range of a regenerative sequence
type: Item
instance of: scholarly article
title: On the range of a regenerative sequence
zbMATH Open document ID: 0573.60083
DOI: 10.1016/0304-4149(85)90019-5
author: Peter W. Glynn
published in: Stochastic Processes and their Applications
publication date: 1985-01-01T00:00:00Z
review text: For a given countable partition of the range of a regenerative sequence \(\{X_ k;k\geq 0\}\) let \(R_ n\) be the number of distinct sets from the partition visited by \(\{X_ k;k\leq n\}\). Under appropriate conditions the limiting behaviour of \(R_ n\) and of \(ER_ n\) is derived and illustrated by examples. The original set up is then broadened to cover the case of a Harris recurrent Markov chain generalizing a result of \textit{L. Chosid} and \textit{R. Isaac}, Ann. Probab. 6, 680-687 (1978; Zbl 0388.60064); Corrections, ibid. 8, 1000 (1980).
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 3915370
zbMATH Keywords: range of a regenerative sequence
zbMATH Keywords: Harris recurrent Markov chain
reviewed by: J. L. Teugels
MaRDI profile type: Publication
full work available at URL: 0304-4149(85)90019-5
OpenAlex ID: W1994873657
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description: scientific article; zbMATH DE number 3915370