Asymptotic behavior of weighted cubic variation of sub-fractional brownian motion. Issue 1 (2nd January 2017) - Kuang, Nenghui
ABSTRACT: In this article, we investigate the convergence of renormalized weighted cubic variation of a sub-fractional Brownian motion S H with Hurst index H . When, we prove by means of Malliavin calculus that the convergence holds in L 2 toward an explicit limit which only depends on S H . We also numerically simulate the sample paths of such a type of sub-fractional Brownian motion regulated by different Hurst index H .