Two inequalities for iterated stochastic integrals

Abstract

Let \( M = (M_{t}, {\mathcal F}_{t})_{t \geq 0} \) be a continuous local martingale with quadratic variation process \( \langle M \rangle \) and \( M_{0} = 0 \) . In this paper, we consider the corresponding sequence of the iterated stochastic integrals \( I_{n}(M) = (I_{n}(t, M), {\mathcal F}_{t})(n \geq 0) \) , defined inductively by