Certain "cadlag" sequences can be decomposed into one of these sequences and an "increasing predictive process" by the Doob-Meyer theorem.
A normal example of these sequences has an underlying sigma  eld equal to sigma of the sign of the W function; that one named for Azema is subject to Kurtz's theorem, which states that one of these things converges if the "Z-hat t" operator for it is self-adjoint. Certain "cadlag" sequences can be decomposed into one of these sequences and an "increasing predictive process" by the Doob-Meyer theorem. Both these sequences and their "super-" generalization are de ned over  ltrations, but in the latter the equals operator has been replaced with a "greater than or equal to" operator in the de nition of EV. An 18th-century strategy in which one repeatedly doubles their bets gives its name to these processes, an example of which is a  nite-dimensional random walk. For 10 points, name these sequences of random variables in which the expected value of one variable equals the observed value of the one previous to it, regardless of other prior observations.
A normal example of these sequences has an underlying sigma  eld equal to sigma of the sign of the W function; that one named for Azema is subject to Kurtz's theorem, which states that one of these things converges if the "Z-hat t" operator for it is self-adjoint.
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