STAT 333 markov_renewal

STAT 333 markov_renewal - Classifying States of a Markov...

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Unformatted text preview: Classifying States of a Markov Chain Definitions : 1. Accessible ( j k )- State k is accessible from state j if it is possible to find a path from state j to k . That is, P ( n ) jk > for some n . 2. Communicate ( j k )- States j and k communicate iff state k is accessible from j and vice-versa. That is, j k and k j . Additionally, communication is an equivalence relation since j j (reflexive) j k implies k j (symmetric) if i j and j k , then i k (transitive) 3. We can partition S (the set of states of the MC) into equivalence/communicating classes. Assign states i and j to the same class if and only if each of these states communicate with each other. There are two types of classes: Closed Class: A communicating class C is closed iff i C and i j implies that j C . Therefore, P ij = 0 for all i C and j / C . Open Class: A communicating class C is open iff for some i C , there exists j / C such that...
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STAT 333 markov_renewal - Classifying States of a Markov...

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