MEXIT: Maximal un-coupling times for stochastic processes

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dc.citation.firstpage355
dc.citation.issueNumber2
dc.citation.journalTitleStochastic Processes and their Applications
dc.citation.lastpage380
dc.citation.volumeNumber129
dc.contributor.authorErnst, Philip A.
dc.contributor.authorKendall, Wilfrid S.
dc.contributor.authorRoberts, Gareth O.
dc.contributor.authorRosenthal, Jeffrey S.
dc.date.accessioned2019-01-24T16:07:55Z
dc.date.available2019-01-24T16:07:55Z
dc.date.issued2019
dc.description.abstractClassical coupling constructions arrange for copies of the same Markov process started at two different initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two different Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this “un-coupling” or “maximal agreement” construction as MEXIT, standing for “maximal exit”. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts.
dc.identifier.citationErnst, Philip A., Kendall, Wilfrid S., Roberts, Gareth O., et al.. "MEXIT: Maximal un-coupling times for stochastic processes." <i>Stochastic Processes and their Applications,</i> 129, no. 2 (2019) Elsevier: 355-380. https://doi.org/10.1016/j.spa.2018.03.001.
dc.identifier.digitalMEXIT
dc.identifier.doihttps://doi.org/10.1016/j.spa.2018.03.001
dc.identifier.urihttps://hdl.handle.net/1911/105118
dc.language.isoeng
dc.publisherElsevier
dc.rightsThis is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subject.keywordAdaptive MCMC
dc.subject.keywordCopula
dc.subject.keywordCoupling
dc.subject.keywordDiffusions
dc.subject.keywordFréchet class
dc.subject.keywordHahn–Jordan decomposition
dc.subject.keywordMarkovian coupling
dc.subject.keywordMCMC
dc.subject.keywordMeet measure
dc.subject.keywordMEXIT
dc.subject.keywordOne-step minorization
dc.subject.keywordPseudo-marginal MCMC
dc.subject.keywordRecognition lemma for maximal coupling
dc.subject.keywordStochastic processes
dc.subject.keywordUn-coupling
dc.titleMEXIT: Maximal un-coupling times for stochastic processes
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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