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A limit theorem for a class of stationary increments Levy moving average process with multiple singularities

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In this paper we present some new limit theorems for power variations of stationary increment Lévy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477–4528, Festschrift for Bernt Øksendal, Stochastics 81(1) (2017), 360–383] under the assumption that the kernel function potentially exhibits a singular behaviour at 0. The aim of this work is to demonstrate how some of the results change when the kernel function has multiple singularity points. Our paper is also related to the article [Stoch. Process. Appl. 125(2) (2014), 653–677] that studied the same mathematical question for the class of Brownian semi-stationary models.

Original languageEnglish
JournalModern Stochastics: Theory and Applications
Pages (from-to)297–316
Number of pages20
Publication statusPublished - Sep 2018

    Research areas

  • Fractional processes, High frequency data, Limit theorems, Lévy processes, Moving averages, Stable convergence, high frequency data, fractional processes, Levy processes, limit theorems, stable convergence, moving averages

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