A Remark on Weighted Cubic Variation of Subfractional Brownian Motion with $H<1/6$
Received:October 12, 2014  Revised:November 24, 2014
Key Words: Subfractional Brownian motion   Malliavin calculus   weighted cubic variation
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11401313), China Postdoctoral Science Foundation (Grant Nos.2014M560368; 2015T80475), the Natural Science Foundation of Jiangsu Educational Committee (Grant No.14KJB110013), 2014 Qing Lan Project, Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No.1401011C), 2013 Jiangsu Government Scholarship for Overseas Studies and Priority Academic Program Development of Jiangsu Higher Education Institutions.
 Author Name Affiliation Junfeng LIU Department of Statistics, Nanjing Audit University, Jiangsu 211815, P. R. China
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In this paper, we prove by means of Malliavin calculus the convergence in $L^2$ of some properly renormalized weighted cubic variation of sub-fractional Brownian motion $S^H$ with parameter $H<\frac16$.