A central limit theorem for the realised covariation of a bivariate\n Brownian semistationary process

2017/07/26 by Andrea Granelli, Granelli, Andrea, Almut E. D. Veraart +1
Economics, Econometrics and Finance · Mathematics · #60F05 #60F15 #60G15 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1707.08507

openalex publication_date 2017/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article presents a weak law of large numbers and a central limit theorem\nfor the scaled realised covariation of a bivariate Brownian semistationary\nprocess. The novelty of our results lies in the fact that we derive the\nsuitable asymptotic theory both in a multivariate setting and outside the\nclassical semimartingale framework. The proofs rely heavily on recent\ndevelopments in Malliavin calculus.\n

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