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


Nenghui Kuang, Bingquan Liu




Let S H,K = {S H,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 t 0 s 0 δ(S H,K (s) − S H,K (r))drds − E t 0 s 0 δ(S H,K (s) − S H,K (r))drds exists in L 2 , where δ(x) is the Dirac delta function for x ∈ R d .