Is this true? I know that if a state is positive recurrent and a MC is irreducible, then all other states are positive recurrent.
To clarify, we are only dealing with finite, countable MC.
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1Yes, if $i$ is recurrent and $i$ communicates with $j$ then $j$ is also recurrent. – Kavi Rama Murthy Nov 26 '20 at 00:06
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and this is true for both null recurrence and positive recurrence? – MinYoung Kim Nov 26 '20 at 00:27
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Yes, it is true. – Kavi Rama Murthy Nov 26 '20 at 05:04