A limit theorem for some linear processes with innovations in the domain of attraction of a stable law

2023/06/19 by Fangjun Xu, Xu, Fangjun · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2306.10893

openalex publication_date 2023/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X=\X_n: n∈ℕ\ be a linear process in which the coefficients are of the form a_i=i^-1ℓ(i) with ℓ being a slowly varying function at the infinity and the innovations are independent and identically distributed random variables belonging to the domain of attraction of an α-stable law with α∈ (1, 2]. We will establish the asymptotic behavior of the partial sum process \∑_n=1^[Nt] X_n: t≥ 0\ as N tends to infinity, where [t] is the integer part of the non-negative number t.

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• Limit Theorems for Tempered Linear Processes with Innovations in the Domain of Attraction of a Stable Law

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