A limit theorem for a class of stationary increments Lévy moving average process with multiple singularities
Volume 5, Issue 3 (2018), pp. 297–316
Pub. online: 20 August 2018
Type: Research Article
Open Access
Open Access
Received
2 March 2018
2 March 2018
Revised
26 June 2018
26 June 2018
Accepted
29 July 2018
29 July 2018
Published
20 August 2018
20 August 2018
Abstract
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.
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