ABSTRACTIn this article, we investigate the convergence of renormalized weighted cubic variation of a sub-fractional Brownian motion SH with Hurst index H. When , we prove by means of Malliavin calculus that the convergence holds in L2 toward an explicit limit which only depends on SH. We also numerically simulate the sample paths of such a type of sub-fractional Brownian motion regulated by different Hurst index H.
['Nenghui Kuang', 'Huantian Xie']
Asymptotic behavior of weighted cubic variation of sub-fractional brownian motion