A functional limit theorem for moving averages with weakly dependent\n heavy-tailed innovations

2020/08/03 by Danijel Krizmanić, Krizmanić, Danijel
Mathematics · #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2008.01592

openalex publication_date 2020/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently a functional limit theorem for sums of moving averages with random\ncoefficients and i.i.d. heavy tailed innovations has been obtained under the\nassumption that all partial sums of the series of coefficients are a.s. bounded\nbetween zero and the sum of the series. The convergence takes place in the\nspace D[0,1] of c `adl `ag functions with the Skorohod M₂ topology.\nIn this article we extend this result to the case when the innovations are\nweakly dependent in the sense of strong mixing and local dependence condition\nD'.\n

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