The generalized Bouleau-Yor identity for a sub-fractional Brownian motion

作     者：YAN LiTan HE Kun CHEN Chao 

作者机构：Department of Mathematics College of Science Donghua University Department of Mathematics East China University of Science and Technology 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第10期

页      面：2089-2116页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 070104[理学-应用数学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11171062) Innovation Program of Shanghai Municipal Education Commission(Grant No.12ZZ063) 

主　　题：sub-fractional Brownian motion Malliavin calculus local time Ito's formula quadratic covaria-tion 

摘      要：Let SH be a sub-fractional Brownian motion with index 0 〈 H 〈 1/2. In this paper we study the existence of the generalized quadratic eovariation [f（SH）, SH]（W） defined by[f（SH）,SH]t（W）=lim ε↓0 1/ ε2H ∫t 0 {f（SH s＋ε）-f（SH s＋ε）-f（SH s）}（SH s＋ε -SH s）ds2H, provided the limit exists in probability, where x → f（x） is a measurable function. We construct a Banach space X of measurable functions such that the generalized quadratic covariation exists in L2 provided f ∈ X. Moreover, the generalized Bouleau-Yor identity takes the form -∫R f（x） H（dx,t）=（2-2 2H-1）[f（SH ）,SH]t（w） for all f ∈ where H （X, t） is the weighted local time of SH. This allows us to write the generalized ItS＇s formula for absolutely continuous functions with derivative belonging to .