CONDITIONAL EXPECTATION AND MARTINGALES
adapted sequence of integrable real-valued random variables, that is, a sequence with the prop-erty that for each n the random variable Xn is measurable relative to Fn and such that EjXnj˙ 1. The sequence X0,X1,... is said to be a martingale relative to the filtration {Fn}n‚0 if it is adapted and if for every n, (1) E(Xn¯1 jFn) ˘ Xn.
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