Renormalized self-intersection local time for sub-bifractional Brownian motion

Abstract

Let SH,K = {SH,K(t), t ? 0} be a d?dimensional sub-bifractional Brownian motion with indices H ? (0, 1) and K ? (0,1]. Assuming d ? 2, as HKd < 1, we mainly prove that the renormalized self-intersection local time ? t0 ? s0 ?(SH,K(s) ? SH,K(r))drds ? E [?t0 ?s0 ?(SH,K(s) ? SH,K(r))drds] exists in L2, where ?(x) is the Dirac delta function for x ? Rd.