假设日B^Hi={Bt^Bi,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B^Hi与B^Hi的相遇局部时,∫t=∫_0^t δ(B_s^H1-B_s^H2)ds,t≥0,其中δ表示Diracdelta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={Bt^Bi,t≥0},i=1,2 be two independent fractional Brownian motions with respective indices Hi∈(0,1). This paper considers the so-called collision local time ∫t=∫_0^t δ(B_s^H1-B_s^H2)ds,t≥0,where δ denotes the Dirac delta function. It is proved that the necessary and sufficient condition for ∫T to be smooth in the sense of the Meyer-Watanabe is rain{H1, H2}〈1/3.