Supermartingale

Summary

A supermartingale is an adapted, integrable stochastic process whose conditional expectation of a future value, given the present information, is at most the present value. It models the fortune of a player in a game that is unfavourable or fair. A process is a supermartingale exactly when its negative is a submartingale. Non-negative supermartingales converge almost surely, a fact used throughout probability and potential theory.