Proving existence results in martingale theory using a subsequence principle

Abstract

New proofs are given of the existence of the compensator of a locally integrable cadlag adapted process of finite variation and of the exis- tence of the quadratic variation process for a cadlag local martingale. Both proofs apply a functional analytic subsequence principle. After presenting the proofs, we discuss their application in giving a simplified account of the con- struction of the stochastic integral of a locally bounded predictable process with respect to a semimartingale.