Show simple item record

dc.contributor.authorHess, Christian
dc.contributor.authorSeri, Raffaello
dc.contributor.authorChoirat, Christine
dc.date.accessioned2014-01-13T08:39:52Z
dc.date.available2014-01-13T08:39:52Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12409
dc.language.isoenen
dc.subjectBirkhoff’s Ergodic Theoremen
dc.subjectAsymptotic mean stationarityen
dc.subjectExtended real-valued random variablesen
dc.subjectNon-integrable random variablesen
dc.subjectCesaro convergenceen
dc.subjectConditional expectationen
dc.subject.ddc519en
dc.titleErgodic theorems for extended real-valued random variablesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe first establish a general version of the Birkhoff Ergodic Theorem for quasi-integrable extended real-valued random variables without assuming ergodicity. The key argument involves the Poincaré Recurrence Theorem. Our extension of the Birkhoff Ergodic Theorem is also shown to hold for asymptotic mean stationary sequences. This is formulated in terms of necessary and sufficient conditions. In particular, we examine the case where the probability space is endowed with a metric and we discuss the validity of the Birkhoff Ergodic Theorem for continuous random variables. The interest of our results is illustrated by an application to the convergence of statistical transforms, such as the moment generating function or the characteristic function, to their theoretical counterparts.en
dc.relation.isversionofjnlnameStochastic Processes and their Applications
dc.relation.isversionofjnlvol120en
dc.relation.isversionofjnlissue10en
dc.relation.isversionofjnldate2010
dc.relation.isversionofjnlpages1908-1919en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.spa.2010.05.008en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record