Lecture 7-8: Martingales and Azuma's Inequality
نویسنده
چکیده
We have seen that if X X1 + · · · + Xn is a sum of independent {0, 1} random variables, then X is tightly concentrated around its expected value [X]. The fact that the random variables were {0, 1}-valued was not essential; similar concentration results hold if we simply assume that they are in some bounded range [−L, L]. One can also relax the independence assumption, as we will see next. Consider a sequence of random variables X0 ,X1 ,X2 , . . .. The sequence {Xi} is called a discretetime martingale if it holds that [Xi+1 | X0 ,X1 , . . . ,Xi] Xi
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