Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion
Abbreviated Journal Title
Probab. Theory Relat. Field
Fractional Brownian motion; Cubic variation; Convergence in law; MULTIPLE STOCHASTIC INTEGRALS; CENTRAL LIMIT-THEOREMS; FUNCTIONALS; Statistics & Probability
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 . 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.
Probability Theory and Related Fields
"Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion" (2014). Faculty Bibliography 2010s. 5114.