Math 564 : Applied Stochastic Processes ( Fall 2017 ) Lecture : 10 Invariant Distributions
نویسندگان
چکیده
Suppose C is a closed recurrent communicating class for a Markov chain, if we restrict the chain on this class, the result is still a Markov chain with state space C. The resulting Markov chain is irreducible and recurrent. In this lecture, we will focus on the long-time behavior of irreducible and recurrent Markov chain. First, we have the following related definition. Definition 10.1. For a Markov chain, a measure ~λ is any row vector (λi, i ∈ I) with non-negative entries. We say that ~λ is invariant if ~λP = ~λ In short, what we will discuss is the invariant measure for probability and expectation.
منابع مشابه
Stochastic Processes ( Fall 2017 ) Lecture : 10 Invariant Distributions
Suppose C is a closed recurrent communicating class for a Markov chain, if we restrict the chain on this class, the result is still a Markov chain with state space C. The resulting Markov chain is irreducible and recurrent. In this lecture, we will focus on the long-time behavior of irreducible and recurrent Markov chain. First, we have the following related definition. Definition 10.1. For a M...
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