noun
martingale
A random process whose expected next value equals its current value given all past information.
Cumulative winnings from fair, fixed-stake coin bets form a martingale.
Etymology
Probability theory borrowed the term from gambling systems called martingales. The mathematical concept formalizes a process with no expected gain from the next step given what is already known.
More examples
- A martingale can rise or fall while its expected next value remains its current value.
- Knowing the entire past does not improve predictions of a martingale's next change.
- Both processes are martingales relative to the same available information.
Forms
martingale · martingales