submartingale

Noun

 * 1)  A stochastic process for which the conditional expectation of future values given the sequence of all prior values is superior or equal to its current value.
 * If a gambler repeatedly plays a game with positive expectation, his payoff over time is a submartingale.

Usage notes

 * A submartingale is a martingale if and only if it is a submartingale and also a supermartingale.