 About 8,730 results  books.google.com Subject to certain additional conditions (and also for chains with continuous time)
, the limit exists also in the usual sense. See Markov chain, ergodk; Markov chain,
class of positive states of a. The transition probabilities p,j{t) for a Markov chain ... 

 books.google.com positive recurrent or they all must be null recurrent. A Markov chain in which all
the states belong to the same communicating class is irreducible. The following
theorems concerning irreducible discretetime Markov chains follow immediately
... 

 books.google.com D Theorem 2.4 reveals that positive recurrence, null recurrence, transience, and
periodicity are all class properties, i.e., ... Corollary 2.2 For an irreducible Markov
chain, either all states are positive recurrent, or all are null recurrent, or all are ... 

 books.google.com FIGURE 54.2 Graph of an infinite irreducible periodic Markov chain of period 3.
where "*" denotes a nonzero element. This is an example of ... A Markov chain is
positive/null recurrent or transient if all its states are positive/null recurrent or
transient, respectively. A regular ... class property. More specifically, the states in
a passage class are transient; in a final class the states are either all positive
recurrent ... 

 books.google.com A Markov chain is said to be irreducible if all states communicate with each other,
that is, there is only one communication class. The states of a ... Transient states
are taken only a finite number of times (because once the communication class of
such a state is left, it cannot be reached again). ... The states of an irreducible
Markov chain are all either positiverecurrent, nullrecurrent or transient. The
states ... 

 books.google.com Recurrence Is a Class Property If i and j communicate, they are either both
recurrent or both transient. Proof. ... An irreducible Markov chain has therefore all
its states of the same nature: transient, positive recurrent, or null recurrent. We
shall ... 

 books.google.com From Facts 4 and 5 one has that, for a communicating class with a finite number
of states, either all the states are transient or all the states are positive recurrent. 7
. From Fact 4 above, if a Markov chain is irreducible, the states are either all ... 

 books.google.com CD Since all communicating classes in a finite state space Markov chain must be
finite, and they must be either closed or not. Theorems 3.7 and 3,8 are ... Hence
states 1, 2, 4, 5, 6 are positive recurrent and state 3 is transient. EXAMPLE 3.11. 

 books.google.com The recurrent and transient states are the same for both chains as well as the
class properties of recurrence and transience. ... A Markov chain is said to be
positive recurrent (respectively null recurrent) if all its states are positive recurrent
... 

 books.google.com One important result is that for any single equivalence class of states, all of those
states are recurrent or all are transient. ... In the former case, the states of the
Markov chain are positive recurrent, and the mean value of the time to return to
state ... 

 