Two inequalities for iterated stochastic integrals

Let M = (M-t, F-t)(t)greater than or equal to0 be a continuous local martingale with quadratic variation process [M] and M-0 = 0. In this paper, we consider the corresponding sequence of the iterated stochastic integrals I-n(M) = (I-n(t, M), F-t)(n greater than or equal to 0), defined inductively by I-n(t, M) = integral(0)(t) In-1(s, M)dM(s) with I-0(t, M) = 1 and I-1(t, M) = M-t. We obtain a maximal inequality at any time and a local time inequality.