Remarks on an integral functional driven by sub-fractional Brownian motion

This paper studies the functionals \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{l}{A_1}\left( {t,x} \right) = \int\limits_0^t {{1_{\left[ {0,\infty } \right)}}} \left( {\chi - S_s^H} \right)ds,\\{A_2}\left( {t,x} \right) = \int\limits_0^t {{1_{\left[ {0,\infty } \right)}}\left( {\chi - S_s^H} \right)} {s^{2H - 2}}ds,\end{array}$$\end{document} where (StH)0≤t≤T is a one-dimension sub-fractional Brownian motion with index H ∈ (0, 1). It shows that there exists a constant pH ∈ (1, 2) such that p-variation of the process Aj(t, StH) − ∫0tℒj(s, SsH)dSsH (j = 1, 2) is equal to 0 if p > pH, where ℒj, j= 1, 2, are the local time and weighted local time of SH, respectively. This extends the classical results for Brownian motion.