Renormalized self-intersection local time of bifractional Brownian motion

Abstract

Let be a d-dimensional bifractional Brownian motion with Hurst parameters and . Assuming , we prove that the renormalized self-intersection local time exists in if and only if , where δ denotes the Dirac delta function. Our work generalizes the result of the renormalized self-intersection local time for fractional Brownian motion.

Existence, renormalization, and regularity properties of higher order derivatives of self-intersection local time of fractional Brownian motion

“…The process which is our focus is fractional Brownian motion. The self-intersection local time of this process was first studied by Rosen in [7], and this has led to a large literature on the subject, including [3,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. A key difficulty with this process, in comparison to ordinary Brownian motion, is that in general the increments of the process are not independent, and this brings considerable complications into the calculations.…”

Correction to: Renormalized self-intersection local time of bifractional Brownian motion

“…In the publication of this article [1], there are five errors. They have now been corrected in this correction.…”