ON THE COLLISION LOCAL TIME OF BIFRACTIONAL BROWNIAN MOTIONS

Abstract

Let [Formula: see text], i = 1,2 be two independent bifractional Brownian motions of dimension 1, with indices Hi ∈ (0, 1) and Ki ∈ (0, 1]. We investigate the collision local time of bifractional Brownian motions [Formula: see text] where δ denotes the Dirac delta function at zero. We show that ℓT exists in L2, and it is Hölder continuous of order 1 - min {H1K1,H2K2}, and furthermore, it is also smooth in the sense of Meyer–Watanabe.