Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise - Archive ouverte HAL Access content directly
Journal Articles Stochastic Processes and their Applications Year : 2022

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

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 $\alpha,\alpha'>0$, 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 $\beta\in(0,1)$. 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 $\alpha<\alpha'\beta$, noise-dominance regime $\alpha>\alpha'\beta$, and critical regime $\alpha = \alpha'\beta$. 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.

Dates and versions

hal-02954467 , version 1 (01-10-2020)

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Olivier Durieu, Yizao Wang. Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise. Stochastic Processes and their Applications, 2022, 143, ⟨10.1016/j.spa.2021.10.007⟩. ⟨hal-02954467⟩
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