Renormalized self-intersection local time of bifractional Brownian motion

摘要

Let BH,K={BH,K(t),t≥0} be a d-dimensional bifractional Brownian motion with Hurst parameters H∈(0,1) and K∈(0,1]. Assuming d≥2, we prove that the renormalized self-intersection local time ∫0T∫0tδ(BH,K(t)−BH,K(s))dsdt−E(∫0T∫0tδ(BH,K(t)−BH,K(s))dsdt) exists in L2 if and only if HKd<3/2, where δ denotes the Dirac delta function. Our work generalizes the result of the renormalized self-intersection local time for fractional Brownian motion.