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Self-stabilizing processes based on random signs
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dc.contributor.author | Falconer, K. J. | |
dc.contributor.author | Lévy Véhel, J. | |
dc.date.accessioned | 2019-09-28T23:37:25Z | |
dc.date.available | 2019-09-28T23:37:25Z | |
dc.date.issued | 2020-03 | |
dc.identifier.citation | Falconer , K J & Lévy Véhel , J 2020 , ' Self-stabilizing processes based on random signs ' , Journal of Theoretical Probability , vol. 33 , no. 1 , pp. 134-152 . https://doi.org/10.1007/s10959-018-0862-9 | en |
dc.identifier.issn | 0894-9840 | |
dc.identifier.other | PURE: 252316577 | |
dc.identifier.other | PURE UUID: fbb707b1-b7fb-45f2-b229-e9cc44a3505b | |
dc.identifier.other | Scopus: 85048531167 | |
dc.identifier.other | ORCID: /0000-0001-8823-0406/work/58055271 | |
dc.identifier.other | WOS: 000530548400006 | |
dc.identifier.uri | https://hdl.handle.net/10023/18576 | |
dc.description.abstract | A 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.format.extent | 19 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Theoretical Probability | en |
dc.rights | Copyright © 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: https://doi.org/10.1007/s10959-018-0862-9 | en |
dc.subject | Self-similar process | en |
dc.subject | Stable process | en |
dc.subject | Localisable process | en |
dc.subject | Multistable process | en |
dc.subject | Poisson point process | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Self-stabilizing processes based on random signs | en |
dc.type | Journal article | en |
dc.description.version | Postprint | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1007/s10959-018-0862-9 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2019-09-29 | |
dc.identifier.url | https://rdcu.be/77og | en |
dc.identifier.url | https://arxiv.org/abs/1802.03231 | en |
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