Definitions
A basic definition of a discrete-time martingale is a discrete-time stochastic process (i.e., a sequence of random variables) X1, X2, X3, ... that satisfies for any time n,
That is, the conditional expected value of the next observation, given all the past observations, is equal to the last observation. Due to the linearity of expectation, this second requirement is equivalent to:
- or
which states that the average "winnings" from observation to observation are 0.
Read more about this topic: Martingale (probability Theory)
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