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The *-Vertex-Reinforced Jump Process

hal.structure.identifierInstitut Camille Jordan [ICJ]
dc.contributor.authorSabot, Christophe
HAL ID: 16397
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorTarres, Pierre
dc.date.accessioned2022-12-09T11:44:42Z
dc.date.available2022-12-09T11:44:42Z
dc.date.issued2022
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/23326
dc.language.isoenen
dc.subject.ddc519en
dc.titleThe *-Vertex-Reinforced Jump Processen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe introduce a non-reversible generalization of the Vertex-Reinforced Jump Process (VRJP), which we call *-Vertex-Reinforced Jump Process (*-VRJP). It can be seen as the continuous-time counterpart of the *-Edge-Reinforced Random Walk (*-ERRW) (see [2,4]), which is itself a non-reversible generalization of the original ERRW introduced by Coppersmith and Diaconis in 1986. In contrast to the classical VRJP, the *-VRJP is not exchangeable after time-change, but we show that with some appropriate randomization of the initial local time, it becomes partially exchangeable after time-change. We provide a representation of the "randomized" *-VRJP as mixture of Markov jump processes with an explicit mixing measure, and show that the "non-randomized" *-VRJP can be written as a mixture of conditioned Markov processes. We also give a counterpart of the β-random potential introduced in [25] for the VRJP, which leads to new identities between integrals.en
dc.publisher.cityParisen
dc.identifier.citationpages53en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris Dauphine-PSLen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2022
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2022-12-09T11:41:32Z
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