Martingale (probability theory)

For the martingale betting strategy, see martingale (betting system).

In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values.

Stopped Brownian motion is an example of a martingale. It can model an even coin-toss betting game with the possibility of bankruptcy.