A short proof of the Doob-Meyer theorem

Stoch Process Their Appl. 2012 Apr;122(4):1204-1209. doi: 10.1016/j.spa.2011.12.001.

Abstract

Every submartingale S of class D has a unique Doob-Meyer decomposition S = M + A , where M is a martingale and A is a predictable increasing process starting at 0. We provide a short proof of the Doob-Meyer decomposition theorem. Several previously known arguments are included to keep the paper self-contained.

Keywords: 60G05; 60G07; Doob–Meyer decomposition; Komlos lemma.