A non-singular version of the Oseledeč ergodic theorem

Dooley, AH; Jin, JIE

A non-singular version of the Oseledeč ergodic theorem

Dooley, AH Jin, JIE

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Publisher:: CAMBRIDGE UNIV PRESS
Publication Type:: Journal Article
Citation:: Ergodic Theory and Dynamical Systems, 2022
Issue Date:: 2022-01-01

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Field	Value	Language
dc.contributor.author	Dooley, AH
dc.contributor.author	Jin, JIE
dc.date.accessioned	2023-02-15T04:59:06Z
dc.date.available	2023-02-15T04:59:06Z
dc.date.issued	2022-01-01
dc.identifier.citation	Ergodic Theory and Dynamical Systems, 2022
dc.identifier.issn	0143-3857
dc.identifier.issn	1469-4417
dc.identifier.uri	http://hdl.handle.net/10453/166146
dc.description.abstract	Kingman's subadditive ergodic theorem is traditionally proved in the setting of a measure-preserving invertible transformation T of a measure space. We use a theorem of Silva and Thieullen to extend the theorem to the setting of a not necessarily invertible transformation, which is non-singular under the assumption that and have the same null sets. Using this, we are able to produce versions of the Furstenberg-Kesten theorem and the Oseledeč ergodic theorem for products of random matrices without the assumption that the transformation is either invertible or measure-preserving.
dc.language	English
dc.publisher	CAMBRIDGE UNIV PRESS
dc.relation.ispartof	Ergodic Theory and Dynamical Systems
dc.relation.isbasedon	10.1017/etds.2021.174
dc.rights	info:eu-repo/semantics/embargoedAccess
dc.subject	0101 Pure Mathematics, 0102 Applied Mathematics, 0802 Computation Theory and Mathematics
dc.subject.classification	General Mathematics
dc.title	A non-singular version of the Oseledeč ergodic theorem
dc.type	Journal Article
utslib.for	0101 Pure Mathematics
utslib.for	0102 Applied Mathematics
utslib.for	0802 Computation Theory and Mathematics
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access	*
utslib.copyright.embargo	2023-09-24T00:00:00+1000Z
dc.date.updated	2023-02-15T04:59:05Z
pubs.publication-status	Published

Abstract:

Kingman's subadditive ergodic theorem is traditionally proved in the setting of a measure-preserving invertible transformation T of a measure space. We use a theorem of Silva and Thieullen to extend the theorem to the setting of a not necessarily invertible transformation, which is non-singular under the assumption that and have the same null sets. Using this, we are able to produce versions of the Furstenberg-Kesten theorem and the Oseledeč ergodic theorem for products of random matrices without the assumption that the transformation is either invertible or measure-preserving.

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http://hdl.handle.net/10453/166146