 About 9,740 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 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 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 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 A transition matrix or Markov chain is said to be positive recurrent if all the states
are so. The following fundamental result ... An irreducible class or chain is
positive recurrent as soon as one ofits states is so. A recurrent class which is not
... 

 books.google.com Describe this (diffusion) process using a Markov chain with 12 states in such a
way that the chain is in state 2(: 1, 2, . . . ,12) ... If for t = 0 the chain is in a state of
the class C1 then, sooner or later, it will be in a state of the class C3 or C4 and
will ... 

 books.google.com If a Markov process has all its states belonging to a single equivalence class, it is
said to be irreducible. For instance ... no restrictions are imposed on the
transitions of {Qn}, it is easy to note that all states of the Markov chain
communicate with each other and hence form a single equivalence class. ... If the
recurrence time is finite, the state (and the class to which it belongs) is known as
positive recurrent. 

 books.google.com Markov. Chain. Theory. A discretetime Markov process on a finite state space Z
specifies the probability of transiting to each state in Z in the next period, ... The
distribution M°° can be interpreted as a selection criterion: over the long run, the
process selects those states on which M°° (z z°) puts positive probability. ... It is
straightforward to show that every finite Markov chain has at least one recurrent
class. 

 books.google.com The semiMarkov chain (Markov renewal chain) is said to be irreducible if there is
only one class. 3. A state i is said to be recurrent ifGii (∞)=1and transient ifGii(∞)
< 1. Arecurrentstatei is positive recurrent if μii < ∞ and null recurrent if μii = ∞. 

 