Construct · 1 fields · 3 citations

martingale: a standalone construct

One name. One construct. A landmark on the map.

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martingale1 CONSTRUCTMartingale processVILLE · FAIR-GAME PROCESS

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Probability theory

A fair-game random process

A model of a fair game: a random process whose expected next value, given everything observed so far, equals its current value, so on average it neither rises nor falls. Ville (1939) coined the term in probability, adapting it from the gambling strategy, and Doob (1953) built the general theory, including the convergence and stopping results that made it central to modern probability and later to the pricing of financial risk. The referent is a sequence of random variables tied together by a conditional-expectation rule, a mathematical object rather than a wagering recipe a player follows or a piece of horse tack.[1][2][3]

Unit
One sequence of random variables satisfying the fair-game condition
Recovery means
Not applicable
Measured by
Verified by checking that the conditional expectation of the next value equals the present value

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Nearby constructs

process3 fields · 3 citationsjingle · one word, three constructsgame2 fields · 3 citationsjingle · one word, two constructsdrift5 fields · 6 citationsjingle · one word, five constructs

References

  1. Ville, J. (1939). Étude critique de la notion de collectif. Gauthier-Villars.
  2. Doob, J. L. (1940). Regularity properties of certain families of chance variables. Transactions of the American Mathematical Society, 47(3), 455–486. https://doi.org/10.1090/s0002-9947-1940-0002052-6
  3. Doob, J. L. (1953). Stochastic processes. Wiley.

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