 About 7,720 results  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 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 If some state were null recurrent, then all the states in the same class, C say,
would be null recurrent, by Theorem 2.4, so that, ... D According to Corollary 2.3,
there must exist at least one positive recurrent class for any finite Markov chain. 

 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 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 We use the expression chain structure to refer to the extent of the decomposition
of the Markov chain into classes. We call a ... This means that, in any closed
irreducible class, all states are either transient, positive recurrent, or null recurrent
. 

 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 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 ... 

 books.google.com Each of the matrices P, represents an irreducible absorbing class, all states
within which are recurrent and accessible to each ... A state / that is positive
recurrent and aperiodic is said to be ergodic, and an irreducible Markov chain
consisting ... 

 books.google.com There are a couple of other useful properties to determine whether or not a class
is positive or null recurrent or transient. The first ... If the state space is finite, we
can be sure that the one class of an irreducible Markov chain is recurrent. This is
... 

 