A maximal inequality for stochastic integrals

摘要

Assume that X is a càdlàg, real-valued martingale startingfrom zero,H is a predictable process with values in [?1; 1] and Y =∫HdX.This article contains the proofs of the following inequalities:(i) If X has continuous paths, thenP(supt-0Yt - 1) ? 2E supt-0