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Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise

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  • Durieu, Olivier
  • Wang, Yizao

Abstract

We consider a stochastic process with long-range dependence perturbed by multiplicative noise. The marginal distributions of both the original process and the noise have regularly-varying tails, with tail indices α,α′>0, respectively. The original process is taken as the regularly-varying Karlin model, a recently investigated model that has long-range dependence characterized by a memory parameter β∈(0,1). We establish limit theorems for the extremes of the model, and reveal a phase transition. In terms of the limit there are three different regimes: signal-dominance regime α<α′β, noise-dominance regime α>α′β, and critical regime α=α′β. As for the proof, we actually establish the same phase-transition phenomena for the so-called Poisson–Karlin model with multiplicative noise defined on generic metric spaces, and apply a Poissonization method to establish the limit theorems for the one-dimensional case as a consequence.

Suggested Citation

  • Durieu, Olivier & Wang, Yizao, 2022. "Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 55-88.
    • Handle: RePEc:eee:spapps:v:143:y:2022:i:c:p:55-88
    DOI: 10.1016/j.spa.2021.10.007
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    References listed on IDEAS

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