A probability distribution of a random variable X is called MEMORYLESS if for non-negative numbers t and s, we have Pr(X>s + t | X > t) = Pr (X > s). Has the POSITIVE MEMORY of a probability distribution ever been defined?
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No, cuz that would imply the generated process from that pdf isn’t adapted to the natural filtration, which isn’t the same as not being memoryless. Just past memory is what we’re trying to measure.
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