Fix t≥s. Then Ms−E[Mt∣Ms] is a non-negative random variable. Its expectation is E[Ms]−E[E[Mt∣Ms]]=E[Ms]−E[Mt]=0. by assumption. Posts about Supermartingale written by George Lowther. English. Etymology. super- + martingale. Noun. supermartingale (plural supermartingales). (mathematics) A martingale in which the random. Tools What links here Related changes Upload file Special pages Permanent link Page information Wikidata item Cite this page. For there star ames escoba no problem, and as expected. The next step is to note that the first integral is with respect to Brownian motion, so has zero expectation. Definition 2 A quasimartingale, Xis an integrable adapted process such that is finite for each time. However, this is not enough to conclude that they are proper martingales.