Joint convergence along different subsequences of the signed cubic   variation of fractional Brownian motion
  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. 
Krzysztof Burdzy, David Nualart, Jason Swanson
math.PR