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dc.contributor.authorFalconer, K. J.
dc.contributor.authorLévy Véhel, J.
dc.identifier.citationFalconer , K J & Lévy Véhel , J 2020 , ' Self-stabilizing processes based on random signs ' , Journal of Theoretical Probability , vol. 33 , no. 1 , pp. 134-152 .
dc.identifier.otherPURE: 252316577
dc.identifier.otherPURE UUID: fbb707b1-b7fb-45f2-b229-e9cc44a3505b
dc.identifier.otherScopus: 85048531167
dc.identifier.otherORCID: /0000-0001-8823-0406/work/58055271
dc.identifier.otherWOS: 000530548400006
dc.description.abstractA self-stabilizing processes {Z(t), t ∈ [t0,t1)} is a random process which when localized, that is scaled to a fine limit near a given t ∈ [t0,t1), has the distribution of an α(Z(t))-stable process, where α:ℝ→(0,2) is a given continuous function. Thus the stability index near t depends on the value of the process at t. In an earlier paper we constructed self-stabilizing processes using sums over plane Poisson point processes in the case of α:ℝ→(0,1) which depended on the almost sure absolute convergence of the sums. Here we construct pure jump self-stabilizing processes when α may take values greater than 1 when convergence may no longer be absolute. We do this in two stages, firstly by setting up a process based on a fixed point set but taking random signs of the summands, and then randomizing the point set to get a process with the desired local properties.
dc.relation.ispartofJournal of Theoretical Probabilityen
dc.rightsCopyright © Springer Science+Business Media, LLC, part of Springer Nature 2018. 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 may differ slightly from the final published version. The final published version of this work is available at:
dc.subjectSelf-similar processen
dc.subjectStable processen
dc.subjectLocalisable processen
dc.subjectMultistable processen
dc.subjectPoisson point processen
dc.subjectQA Mathematicsen
dc.titleSelf-stabilizing processes based on random signsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.description.statusPeer revieweden

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