Self-stabilizing processes
Abstract
We 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.
Citation
Falconer , K J & Lévy Vehel , J 2018 , ' Self-stabilizing processes ' , Stochastic Models , vol. 34 , no. 4 , pp. 409-434 . https://doi.org/10.1080/15326349.2018.1521726
Publication
Stochastic Models
Status
Peer reviewed
ISSN
1532-6349Type
Journal article
Rights
Copyright © 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 https://doi.org/10.1080/15326349.2018.1521726
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