[*AMS 2010 subject classifications.*]{} Primary  60F05,  60F15,  60G22; Secondary  60G48,  60H05.
author:
- 'Andreas Basse-O’Connor[^1]'
- 'Raphaël Lachièze-Rey[^2]'
- 'Mark Podolskij[^3]'
title: |
    Limit theorems for\
    stationary increments Lévy driven moving averages
---

Introduction and main results {#Intro}
=============================

In the recent years there has been an increasing interest in limit theory for power variations of stochastic processes. Power variation functionals and related statistics play a major role in analyzing the fine properties of the underlying model, in stochastic integration concepts and statistical inference. In the last decade asymptotic theory for power variations of various classes of stochastic processes has been intensively investigated in the literature. We refer e.g.  to [@BGJPS; @J; @JP; @PV] for limit theory for power variations of Itô semimartingales, to [@BNCP09; @BNCPW09; @Coeu; @gl89; @nr09] for the asymptotic results in the framework of fractional Brownian motion and related processes, and to [@Rosenblatt; @Rosenblatt-1] for investigations of power variation of the Rosenblatt process.

In this paper we study the power variation of *stationary increments Lévy driven moving averages*. More specifically, we consider an infinitely divisible process with stationary increments $(X_t)_{t\geq 0}$, defined on a probability space $(\Omega, \mathcal F,   \mathbb P)$, given as $$\begin{aligned}
 \label{def-of-X-43}
X_t= \int_{-\infty}^t 