DC FieldValueLanguage
dc.contributor.authorFoss, Sergey-
dc.contributor.authorSchulte, Matthias-
dc.date.accessioned2021-10-08T08:17:39Z-
dc.date.available2021-10-08T08:17:39Z-
dc.date.issued2021-09-20-
dc.identifier.citationStochastic Processes and their Applications 142: 432-461 (2021-12-01)de_DE
dc.identifier.issn0304-4149de_DE
dc.identifier.urihttp://hdl.handle.net/11420/10471-
dc.description.abstractWe examine the influence of using a restart mechanism on the stationary distributions of a particular class of Markov chains. Namely, we consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoregressive coefficient tends to one, the noise scaling parameter tends to zero, and the neighbourhood size varies. We show that the restart mechanism may change significantly the limiting distribution. We obtain a limit theorem with a novel type of limiting distribution, a mixture of an atomic distribution and an absolutely continuous distribution whose marginals, in turn, are mixtures of distributions of signed absolute values of normal random variables. In particular, we provide conditions for the limiting distribution to be normal, like in the case without restart mechanism. The main theorem is accompanied by a number of examples and auxiliary results of their own interest.en
dc.language.isoende_DE
dc.publisherElsevierde_DE
dc.relation.ispartofStochastic processes and their applicationsde_DE
dc.subjectAutoregressive modelde_DE
dc.subjectCharacteristic functionde_DE
dc.subjectLimiting distributionde_DE
dc.subjectNormal distributionde_DE
dc.subjectRestart mechanismde_DE
dc.subjectStationary distributionde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleNon-standard limits for a family of autoregressive stochastic sequencesde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishWe examine the influence of using a restart mechanism on the stationary distributions of a particular class of Markov chains. Namely, we consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoregressive coefficient tends to one, the noise scaling parameter tends to zero, and the neighbourhood size varies. We show that the restart mechanism may change significantly the limiting distribution. We obtain a limit theorem with a novel type of limiting distribution, a mixture of an atomic distribution and an absolutely continuous distribution whose marginals, in turn, are mixtures of distributions of signed absolute values of normal random variables. In particular, we provide conditions for the limiting distribution to be normal, like in the case without restart mechanism. The main theorem is accompanied by a number of examples and auxiliary results of their own interest.de_DE
tuhh.publisher.doi10.1016/j.spa.2021.09.006-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.volume142de_DE
tuhh.container.startpage432de_DE
tuhh.container.endpage461de_DE
dc.identifier.scopus2-s2.0-85115977331de_DE
local.status.inpressfalsede_DE
local.funding.infoThe work is supported in part by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation.de_DE
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.creatorGNDFoss, Sergey-
item.creatorGNDSchulte, Matthias-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidFoss, Sergey-
item.creatorOrcidSchulte, Matthias-
item.languageiso639-1en-
item.mappedtypeArticle-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0003-0116-5846-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
Appears in Collections:Publications without fulltext
Show simple item record

Page view(s)

59
Last Week
1
Last month
6
checked on Aug 15, 2022

Google ScholarTM

Check

Add Files to Item

Note about this record

Cite this record

Export

Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.