Limit theorems for multivariate Brownian semistationary processes and feasible results

Riccardo Passeggeri, Almut E.D. Veraart

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In this paper we introduce the multivariate Brownian semistationary (BSS) process and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for general multivariate Gaussian processes with stationary increments, which are not necessarily semimartingales. Then, we show weak laws of large numbers, central limit theorems, and feasible results for BSS processes. An explicit example based on the so-called gamma kernels is also provided.

Original languageEnglish
JournalAdvances in Applied Probability
Pages (from-to)667-716
Number of pages50
Publication statusPublished - 1 Sept 2019
Externally publishedYes


  • central limit theorem
  • feasible
  • gamma kernel
  • high frequency data
  • intermittency
  • law of large numbers
  • Multivariate Brownian semistationary process
  • nonsemimartingale
  • Wiener chaos


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