Forward and symmetric Wick-Itôintegrals with respect to fractional Brownian motion  

作　　者：Fuquan XIA Litan YAN Jianhui ZHU 

机构地区：[1]Department of Mathematics,College of Science,Bengbu University,Bengbu 233030,China [2]Department of Statistics,College of Science,Donghua University,Shanghai 201620,China

出　　处：《Frontiers of Mathematics in China》2021年第2期623-645,共23页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported in part by the National Natural Science Foundation of China(Grant No.11971101).

摘　　要：Let BH={BHt,t≥0}be a fractional Brownian motion with Hurst index H∈(0,1).Inspired by pathwise integrals and Wick product,in this paper,we consider the forward and symmetric Wick-Itôintegrals with respect to BH as follows:∫t0us⋄d−BHs=limε↓01ε∫t0us⋄(BHs+ε−BHs)ds,∫t0us⋄d∘BHs=limε↓012ε∫t0us⋄(BHs+ε−BH(s−ε)∨0)ds,in probability,where◊denotes the Wick product.We show that the two integrals coincide with divergence-type integral of BH for all H∈(0,1).

关 键 词：Fractional Brownian motion(fBm) forward integral Malliavin calculus Wick product 

分 类 号：O17[理学—数学]