Let S = {（St1,···,Std ）}t≥0 denote a d-dimensional sub-fractional Brownian motion with index H ≥ 1/2. In this paper we study some properties of the process X of the formwhere Rt = （（St1）2＋···＋（Std）2）~1/2 is the sub-fractional Bessel process.
假设B^H_i={B_t^(H_i),t≥0},i=1,2是两个独立的分数布朗运动,其指数分别为Hi∈(0,1)。文中考虑BH1与BH2的相遇局部时,lt=integral from n=0 to 1( δ (B_s^H-B_s^H)ds),t≥0,其中δ表示Dirac delta函数。证明此局部时在Meyer-Watanabe意义下是光滑的充分必要条件为min{H1,H2}<1/3。
Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and Wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.
SHEN GuangJun 1,2,& YAN LiTan 3 1 Department of Mathematics,East China University of Science and Technology,Shanghai 200237,China
