A limit theorem for moving averages in the \(\alpha\)-stable domain of attraction

DOI10.1016/j.spa.2013.10.006zbMath1314.60085arXiv1212.1372OpenAlexW2142265357MaRDI QIDQ2434756

Bojan Basrak, Danijel Krizmanić

Publication date: 7 February 2014

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.1372

zbMATH Keywords

regular variationfunctional limit theoremmoving average processstable Lévy process\(M_2\) topology

Mathematics Subject Classification ID

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

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An invariance principle for sums and record times of regularly varying stationary sequences ⋮ Maxima of linear processes with heavy‐tailed innovations and random coefficients ⋮ A large deviations approach to limit theory for heavy-tailed time series ⋮ A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations ⋮ Joint functional convergence of partial sums and maxima for linear processes ⋮ Convergence to a Lévy process in the Skorohod \(\mathcal{M}_1\) and \(\mathcal{M}_2\) topologies for nonuniformly hyperbolic systems, including billiards with cusps ⋮ On partial-sum processes of ARMAX residuals ⋮ Functional convergence for moving averages with heavy tails and random coefficients ⋮ A functional limit theorem for moving averages with weakly dependent heavy-tailed innovations

Cites Work

• A functional limit theorem for dependent sequences with infinite variance stable limits
• Limit theorems for sums of linearly generated random variables
• Functional limit theorems for linear processes in the domain of attraction of stable laws
• Limit theory for moving averages of random variables with regularly varying tail probabilities
• Weak convergence of sums of moving averages in the \(\alpha\)-stable domain of attraction
• Stochastic-Process Limits
• Heavy-Tail Phenomena

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