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 NA giving the number of times the chain passes through the set A, i.e.
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Classification of Markov chains
Asymptotic behavior of Markov chains
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