## Bernoulli

• Bernoulli
• Volume 25, Number 3 (2019), 2245-2278.

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

#### Abstract

This article presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of our results lies in the fact that we derive the suitable asymptotic theory both in a multivariate setting and outside the classical semimartingale framework. The proofs rely heavily on recent developments in Malliavin calculus.

#### Article information

Source
Bernoulli, Volume 25, Number 3 (2019), 2245-2278.

Dates
Revised: June 2018
First available in Project Euclid: 12 June 2019

https://projecteuclid.org/euclid.bj/1560326444

Digital Object Identifier
doi:10.3150/18-BEJ1052

Mathematical Reviews number (MathSciNet)
MR3961247

Zentralblatt MATH identifier
07066256

#### Citation

Granelli, Andrea; Veraart, Almut E.D. A central limit theorem for the realised covariation of a bivariate Brownian semistationary process. Bernoulli 25 (2019), no. 3, 2245--2278. doi:10.3150/18-BEJ1052. https://projecteuclid.org/euclid.bj/1560326444

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#### Supplemental materials

• Supplement to “A central limit theorem for the realised covariation of a bivariate Brownian semistationary process”. We collect technical details and proofs in the supplementary article, which should be read in conjunction with the present paper.