Hidden regular variation of moving average processes with heavy-tailed innovations

Resnick, Sidney I.; Roy, Joyjit

doi:10.1239/jap/1417528480

Cited by 2 publications

(1 citation statement)

References 21 publications

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“…Here δ 0 denotes the Dirac measure putting unit mass at 0. Examples where the limit measures are not concentrated on the axes were considered in Resnick & Roy [36]. They investigated the corresponding regular variation property for stationary moving average processes with positive regularly varying innovations and positive coefficients and computed the limit measure explicitly.…”

Section: Preliminaries and Main Resultsmentioning

confidence: 99%

Branching random walks, stable point processes and regular variation

Bhattacharya¹,

Hazra²,

Roy³

2018

Stochastic Processes and their Applications

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Abstract. Using the language of regular variation, we give a sufficient condition for a point process to be in the superposition domain of attraction of a strictly stable point process. This sufficient condition is then used to obtain the weak limit of a sequence of point processes induced by a branching random walk with jointly regularly varying displacements. Because of heavy tails of the step size distribution, we can invoke a one large jump principle at the level of point processes to give an explicit representation of the limiting point process. As a consequence, we extend the main result of Durrett [18] and verify that two related predictions of Brunet & Derrida [14] remain valid for this model.

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Section: Preliminaries and Main Resultsmentioning

confidence: 99%

Branching random walks, stable point processes and regular variation

Bhattacharya¹,

Hazra²,

Roy³

2018

Stochastic Processes and their Applications

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show abstract

Extremes of multitype branching random walks: heaviest tail wins

et al. 2019

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We consider a branching random walk on a multi(Q)-type, supercritical Galton-Watson tree which satisfies Kesten-Stigum condition. We assume that the displacements associated with the particles of type Q have regularly varying tails of index α, while the other types of particles have lighter tails than that of particles of type Q. In this article, we derive the weak limit of the sequence of point processes associated with the positions of the particles in the n th generation. We verify that the limiting point process is a randomly scaled scale-decorated Poisson point process (SScDPPP) using the tools developed in [10]. As a consequence, we shall obtain the asymptotic distribution of the position of the rightmost particle in the n th generation.

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Hidden regular variation of moving average processes with heavy-tailed innovations

Cited by 2 publications

References 21 publications

Branching random walks, stable point processes and regular variation

Branching random walks, stable point processes and regular variation

Extremes of multitype branching random walks: heaviest tail wins

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