Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion

Krzysztof Burdzy, David Nualart, Jason Swanson

Published 2012-10-04Version 1

The purpose of this paper is to study the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter $H=1/6$. We prove that, under some conditions on both subsequences, the limit is a two-dimensional Brownian motion whose components may be correlated and we find explicit formulae for its covariance function.