Strong Markov Property
Suppose that is a stochastic process on a probability space with natural filtration . Then is said to have the strong Markov property if, for each stopping time, conditioned on the event, the process (which maybe needs to be defined) is independent from and has the same distribution as for each .
The strong Markov property is a stronger property than the ordinary Markov property, since by taking the stopping time, the ordinary Markov property can be deduced.
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