Stationary measures for continuous time markov chain

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Why in every textbook stationary measures are defined only for recurrent and irreducible Markov chains?
I have a Markov chain model and without determining it's irreducibility and positive recurrency I could find it's stationary measures.
So my question is: What is the definition of invariant measures or stationary measures for a general Markov chain?




markov-chains




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    up vote
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    down vote

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    Why in every textbook stationary measures are defined only for recurrent and irreducible Markov chains?
    I have a Markov chain model and without determining it's irreducibility and positive recurrency I could find it's stationary measures.
    So my question is: What is the definition of invariant measures or stationary measures for a general Markov chain?




    markov-chains




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Why in every textbook stationary measures are defined only for recurrent and irreducible Markov chains?
      I have a Markov chain model and without determining it's irreducibility and positive recurrency I could find it's stationary measures.
      So my question is: What is the definition of invariant measures or stationary measures for a general Markov chain?




      markov-chains




      share|cite|improve this question











      Why in every textbook stationary measures are defined only for recurrent and irreducible Markov chains?
      I have a Markov chain model and without determining it's irreducibility and positive recurrency I could find it's stationary measures.
      So my question is: What is the definition of invariant measures or stationary measures for a general Markov chain?





      markov-chains





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Aug 3 at 20:40









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