Two inequalities for iterated stochastic integrals

摘要

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