Remarks on an integral functional driven by sub-fractional Brownian motion

This paper studies the functionals A(1) (t, x) = integral(t)(0) 1([0,infinity))(x - S-s(H))ds, A(2)(t, x) = integral(t)(0) 1([0,infinity))(x - S-s(H))s(2H-1)ds, where (S-t(H))(0 <= t <= T) is a one-dimension sub-fractional Brownian motion with index H is an element of (0, 1). It shows that there exists a constant P-H is an element of (1, 2) such that p-variation of the process A(j)(t, S-t(H)) - integral(t)(0) L-j(s, S-s(H))dS(s)(H) (j = 1, 2) is equal to 0 if p > p(H), where L-j = 1, 2, are the local time and weighted local time of S-H, respectively. This extends the classical results for Brownian motion. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.