Asymptotic behavior of weighted cubic variation of sub-fractional brownian motion. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Kuang, Nenghui; Xie, Huantian
• Is Part Of: Communications in statistics. Volume 46:Issue 1(2017)
• Page Start: 215
• Page End: 229
• Publication Date: 2017-01-02
• Subjects: Malliavin calculus -- Sub-fractional Brownian motion -- Weighted cubic variation; 60H07 -- 60G15 -- 60G22; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2014.957849
• Languages: English
• ISSNs: 0361-0918

Abstract

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 .