We study the asymptotic behavior of the sequence as tends to infinity, where and are two independent subfractional Brownian motions with indices and , respectively. is a kernel function and the bandwidth parameter satisfies some hypotheses in terms of and . Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motion . We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion.
Yuquan Cang. Junfeng Liu. Yan Zhang. "Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus." Abstr. Appl. Anal. 2014 (SI35) 1 - 14, 2014. https://doi.org/10.1155/2014/635917