Functional convergence of linear processes with heavy-tailed innovations

DOI10.1007/s10959-014-0581-9zbMath1346.60037arXiv1410.3115OpenAlexW2111977200WikidataQ59465418 ScholiaQ59465418MaRDI QIDQ300283

Adam Jakubowski, Sana Louhichi, Raluca M. Balan

Publication date: 27 June 2016

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.3115

zbMATH Keywords

partial sum processlinear processesstable processesLévy motionfunctional convergence

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Central limit and other weak theorems (60F05) Stable stochastic processes (60G52) Functional limit theorems; invariance principles (60F17)

Related Items (13)

Invariance principles for tempered fractionally integrated processes ⋮ An invariance principle for sums and record times of regularly varying stationary sequences ⋮ Limit theorems for linear random fields with innovations in the domain of attraction of a stable law ⋮ Maxima of linear processes with heavy‐tailed innovations and random coefficients ⋮ A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations ⋮ Discrete-time trawl processes ⋮ Limit theorems for functionals of long memory linear processes with infinite variance ⋮ Unnamed Item ⋮ Joint functional convergence of partial sums and maxima for linear processes ⋮ New characterizations of the \(S\) topology on the Skorokhod space ⋮ A note on the normalizing sequences for sums of linear processes in the case of negative memory ⋮ On functional limits of short- and long-memory linear processes with GARCH(1,1) noises ⋮ A functional limit theorem for moving averages with weakly dependent heavy-tailed innovations

Uses Software

• itsmr

Cites Work

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