Do the notions of null or positive recurrence have to be defined with respect to irreducible, aperiodic chains or does irreducibility suffice?
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Sorry but after your rapid succession of basic questions on the subject, one needs to know: are you following a textbook? If not, why? – Did Dec 31 '18 at 20:26
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@Did I am following a textbook and that is where this question came from. In Lawler's Stochastic Processes, Chapter 2 defines null and positive recurrence only for irreducible, aperiodic chains, which is why I wonder whether periodicity is needed here? – p-value Jan 01 '19 at 07:01
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@Did Ditto for the other two questions I posed; I was not able to find an answer to either on the book. If you could point me to a resource or post an answer, I would gladly accept it. – p-value Jan 01 '19 at 07:04
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The trouble is that you seem to stumble on very basic obstacles, well below the subject you are trying to tackle... hence my advice for a reference would be a mildly general and mildly complete textbook on probability theory (say, Durrett), to be worked on thoroughly before continuing the present string of essentially irrelevant questions. – Did Jan 01 '19 at 11:41