p-variation of an integral functional driven by fractional Brownian motion

摘要

Let (B-t(H))(0 <= t <= T) be a one-dimensional fractional Brownian motion with Hurst parameter H is an element of (0, 1). We study the functionals A(1)(t, x) = integral(t)(0)1([0,infinity)) (x - B-s(H))s(2H-1)ds, A(2)(t, x) = integral(0)1([0,infinity)) (x - B-s(H))ds. We show that there exists a constant p(H) is an element of (1, 2) depending only on H such that the p-variation of A(j) (t, B-t(H)) - integral(t)(0) L-j(s, B-s(H))dB(s)(H) (j = 1, 2) is zero if p > p(H), where L-1, L-2 are the local time and weighted local time of B-H, respectively. This extends the illustrated result for Brownian motion.