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dc.contributor.authorFalconer, K. J.
dc.contributor.authorLévy Vehel, J.
dc.identifier.citationFalconer , K J & Lévy Vehel , J 2018 , ' Self-stabilizing processes ' , Stochastic Models , vol. 34 , no. 4 , pp. 409-434 .
dc.identifier.otherPURE: 252309522
dc.identifier.otherPURE UUID: 4cc6e214-4533-4b8a-832b-943c063ed8fd
dc.identifier.otherScopus: 85057216071
dc.identifier.otherORCID: /0000-0001-8823-0406/work/58055245
dc.identifier.otherWOS: 000461881300003
dc.description.abstractWe construct "self-stabilizing" processes {Z(t), t ∈[t0,t1)}. These are random processes which when "localized", that is scaled around t to a fine limit, have the distribution of an α(Z(t))-stable process, where α is some given function on ℝ. Thus the stability index at t depends on the value of the process at t. Here we address the case where α: ℝ → (0,1). We first construct deterministic functions which satisfy a kind of autoregressive property involving sums over a plane point set Π. Taking Π to be a Poisson point process then defines a random pure jump process, which we show has the desired localized distributions.
dc.relation.ispartofStochastic Modelsen
dc.rightsCopyright © 2018 Taylor & Francis Group, LLC This work has been made available online in accordance with the publisher’s policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at
dc.subjectLocal formen
dc.subjectStable processen
dc.subjectQA Mathematicsen
dc.titleSelf-stabilizing processesen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.description.statusPeer revieweden

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