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Bookmark or Share- Chapter 5 Martingales. - New York UniversityThe theory of martingales plays a very important ans ueful role in the study of stochastic processes. A formal definition is given below. Definition 5.1. Let (Ω, F, P ) be a probability space. A martingale se-quence of length n is a chain X 1, X 2, , Xn of random variables and corre-. · · ·.
- 1 Defining martingales - MIT OpenCourseWare1 Defining martingales. Let S be a sample space. Let X0, X1, X2, . . . be a sequence of random variables. Informally, we will imagine that we are acquiring information about S in a sequence of stages, and the random variable Xn is a quantity that is known to us at the nth stage. If Z is any random variable, let. E[Z|Fn]
- Martingale - Encyclopedia of MathematicsThe game-theoretic sense of the function $ V _ {k} $ defined by (2) is that the player doubles his stake when he loses and stops the game on his first win. In the gambling world such a system is called a martingale, which explains the origin of the mathematical term "martingale" .
- Martingale Definition & Meaning - Merriam-WebsterThe meaning of MARTINGALE is a device for steadying a horse's head or checking its upward movement that typically consists of a strap fastened to the girth, passing between the forelegs, and bifurcating to end in two rings through which the reins pass.
- Martingales - Yale UniversityIf (X t ,ℱ t) is a martingale and T is a stopping time for {ℱ t }, then for any n∈ℕ, E [X min (T,n)] = E [X 0 ]. Proof. Define Y t = >. Then (Y t ,ℱ t) is a martingale since we can treat [T≤t-1] as a sequence of bets.
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