2. Classification of Markov chains
One of the most remarkable features of Markov chains is their close resemblance to the 0 or 1 law for independent random variables. We will show that, starting from a point x, the chain will visit this point an infinite number of times with a probability that can only be equal to 0 or 1. We will then see that these two types of behavior cannot coexist for different starting points, if we impose a property of irreducibility.
2.1 Recurrence and transience
In the context of a canonical chain, we use the definitions of successive entry times and return times given in Definition 7, and add the random variable N A giving the number of times the chain passes through the set A, i.e.
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Classification of Markov chains
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