A note on joint functional convergence of partial sum and maxima for\n linear processes

2018/03/06 by Danijel Krizmanić, Krizmanic, Danijel
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Mathematical Inequalities and Applications #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1803.02141

openalex publication_date 2018/03/06 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Recently, for the joint partial sum and partial maxima processes constructed\nfrom linear processes with independent identically distributed innovations that\nare regularly varying with tail index \α \∈ (0, 2), a functional limit\ntheorem with the Skorohod weak M₂ topology has been obtained. In this\npaper we show that, if all the coefficients of the linear processes are of the\nsame sign, the functional convergence holds in the stronger topology, i.e. in\nthe Skorohod weak M₁ topology on the space of \ℝ²--valued\nc `adl `ag functions on [0, 1].\n

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