一类双分数Brownian运动的广义二次协变差

假设B是一个指数为H∈(0,1),K∈(,1]且满足2HK＜1的双分数Brownian运动,其赋权局部时设为{(b)(x,t),t≥0,x∈R}.建立了f(B)与B的广义二次协变差f(B),B](W),并且研究如下局部时的积分∫Rf(x)(b)(dx,t), t≥0,这里x|→f(x)为Borel可测函数.构造了一个B...

The generalized quadratic covariation for a bi-fBm

Let B be a bi - fractional Brownian motion with indices H ∈ (0,1),K ∈ (0,1 ] such that 2HK＜ 1,and let ｛(b)(x,t),t≥0,x ∈ R ｝ be its local time process.The generalized quadratic covariation [f(B),B] (W) off(B) and B is introduced.The integral∫Rf( x )（b）( dx,t ), t ≥ 0is studied,where x ｜→f(x) is a Borel measurable function.A Banach space (H)is constructed,which satisfies the generalized quadratic covariation exists in L2 and the generalized Bouleau -Yor identity takes the form [f(B),B]t(W) =- 21-K∫Rf(x)L(dx,t), t ≥ 0for all f∈ (H).Thereby,the generalized It(o) formula tor absolutely continuous functions with derivatives belonging to (H) is investiagted.As an application,the It(o) - Tanaka formula for the bi - fractional Brownian motion with 2HK ＜ 1 is obtained.