A limit theorem for a class of stationary increments L\'{e}vy moving average process with multiple singularities
Abstract
In this paper we present some new limit theorems for power variations of stationary increment L\'{e}vy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477--4528, Festschrift for Bernt {\O}ksendal, Stochastics 81(1) (2017), 360--383] under the assumption that the kernel function potentially exhibits a singular behaviour at . 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.
Cite
@article{arxiv.1803.01017,
title = {A limit theorem for a class of stationary increments L\'{e}vy moving average process with multiple singularities},
author = {Mathias Mørck Ljungdahl and Mark Podolskij},
journal= {arXiv preprint arXiv:1803.01017},
year = {2018}
}
Comments
Published at https://doi.org/10.15559/18-VMSTA111 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)