"Limit theorems for multipower variation in the presence of jumps"

Ole E. Barndorff-Nielsen
Department of Mathematical Sciences,
University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark

Neil Shephard
Nuffield College, University of Oxford, Oxford OX1 1NF, UK

and

Matthias Winkel
Department of Statistics, University of Oxford, 
1 South Parks Road, Oxford OX1 3TG, U.K. 

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.

Keywords: Bipower variation; Infinite activity; Multipower variation; Power variation; Quadratic variation; Semimartingales; Stochastic volatility.