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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 ...
A martingale is a class of betting strategies that originated from and were popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins the stake if a coin comes up heads and loses if it comes up tails.
Martingale (betting system), in 18th century France; a dolphin striker, a spar aboard a sailing ship; In the sport of fencing, a martingale is a strap attached to the sword handle to prevent a sword from being dropped if disarmed; In the theatrical lighting industry, martingale is an obsolete term for a twofer, or occasionally a threefer
In mathematics, a local martingale is a type of stochastic process, satisfying the localized version of the martingale property. Every martingale is a local martingale; every bounded local martingale is a martingale; in particular, every local martingale that is bounded from below is a supermartingale, and every local martingale that is bounded from above is a submartingale; however, a local ...
A variation of the standing martingale, called a tiedown, is seen almost exclusively in the western riding disciplines. A tiedown is adjusted much shorter than a standing martingale and is intended primarily to prevent the horse from flipping its head up when asked to abruptly stop or turn in speed events.
In the mathematical theory of probability, a Doob martingale (named after Joseph L. Doob, [1] also known as a Levy martingale) is a stochastic process that approximates a given random variable and has the martingale property with respect to the given filtration. It may be thought of as the evolving sequence of best approximations to the random ...
The martingale central limit theorem generalizes this result for random variables to martingales, which are stochastic processes where the change in the value of the process from time t to time t + 1 has expectation zero, even conditioned on previous outcomes.
The martingale representation theorem can be used to establish the existence of a hedging strategy. Suppose that () < is a Q-martingale process, whose volatility is always non-zero.