Functional Convergence of Linear Processes with Heavy-Tailed Innovations

2014/10/12 by Raluca M. Balan, Balan, Raluca M., Adam Jakubowski +3 · 1 citation
Mathematics · #60F17 #60G52 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F17 #msc:60G52

paper · pdf · doi:10.48550/arxiv.1410.3115

39 pages; revised version of arxiv 1209.1147

arxiv created 2014/10/12 · arxiv updated 2014/10/14

Abstract

We study convergence in law of partial sums of linear processes with heavy-tailed innovations. In the case of summable coefficients necessary and sufficient conditions for the finite dimensional convergence to an α-stable Lévy Motion are given. The conditions lead to new, tractable sufficient conditions in the case α≤ 1. In the functional setting we complement the existing results on M₁-convergence, obtained for linear processes with nonnegative coefficients by Avram and Taqqu (1992) and improved by Louhichi and Rio (2011), by proving that in the general setting partial sums of linear processes are convergent on the Skorokhod space equipped with the S topology, introduced by Jakubowski (1997).

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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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