REGULARITY OF RENORMALIZED SELF-INTERSECTION LOCAL TIME FOR FRACTIONAL BROWNIAN MOTION

摘要

Let B_t~H be a d-dimensional fractional Brownian motion with Hurst parameter H ∈ (0, 1). We study the regularity, in the sense of the Malliavin calculus, of the renormalized self-intersection local timernl = ∫_0~T ∫_0~t δ_0(B_t~H - B_s~H)dsdt - E(∫_0~T ∫_0~t δ_0(B_t~H - B_s~H)dsdt)rnwhere δ_0 is the Dirac delta function.