Limit theorems for multipower variation in the presence of jumps

Ole E. Barndorff-Nielsen: Department of Mathematical Sciences,
University of Aarhus

Neil Shephard: Nuffield College, University of Oxford

Matthias Winkel: Department of Statistics, University of Oxford, 

Abstract

In this paper we provide a systematic study of the robustness of probability limits and central limit theory for realised multipower variation when we add finite activity and infinite activity jump processes to an underlying Brownian semimartingale. 

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