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Title: On non-ergodic versions of limit theorems (English)
Author: Volný, Dalibor
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 34
Issue: 5
Year: 1989
Pages: 351-363
Summary lang: English
Summary lang: Russian
Summary lang: Czech
Category: math
Summary: The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds. (English)
Keyword: central limit theorem for martingale differences
Keyword: ergodic decomposition
Keyword: invariance principle
Keyword: invariant measure
Keyword: law of iterated logarithm
Keyword: strictly stationary sequence
MSC: 28D05
MSC: 60B10
MSC: 60F05
MSC: 60F17
MSC: 60G10
MSC: 60G40
idZBL: Zbl 0707.60027
idMR: MR1014076
DOI: 10.21136/AM.1989.104363
Date available: 2008-05-20T18:37:18Z
Last updated: 2020-07-28
Stable URL:
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