2
$\begingroup$

Question

Consider the following transition matrix:

 P= 
 0     0     1     0     0     0 
 0     0     0     0     0     1
 0     0     0     0     1     0
1/4   1/4    0    1/2    0     0
 1     0     0     0     0     0
 0    1/3    0     0     0    2/3

a) Which states are transient? b) Which states are recurrent? c) Identify all closed sets of states. d) Is this chain ergodic?

Dear friends ,

I have thought the states are as follows, {1,5} {0,2,4} recurrent since they communicate with each other {3} transient

and since state 3 does not communicate with other states, it is not an ergodic Mc

Am I correct?

Thank you..

$\endgroup$
  • 1
    $\begingroup$ What is your reasoning? PS Please format your question for readability; see stats.stackexchange.com/editing-help. $\endgroup$ – whuber Mar 16 '13 at 3:03
  • $\begingroup$ Dear @whuber , I don't know how to write matrix.It is not mentioned in the link also :/ $\endgroup$ – StocSim Mar 16 '13 at 10:42
  • $\begingroup$ I have at least roughly fixed the matrix for you, by selecting the text for the matrix and then clicking on the $\{\}$ symbol to make it monospaced text and then lining it up. $\endgroup$ – Glen_b -Reinstate Monica Mar 16 '13 at 11:22
  • 1
    $\begingroup$ Stochastic processes is a subject of statistics rather than 'math' math is deterministic,stat is stochastic. thx $\endgroup$ – StocSim Mar 16 '13 at 17:32
  • 2
    $\begingroup$ @StocSim I think the relevant determinant of what makes a question appropriate on CV is the scope given in the faq; that would be the basis on which to argue that it belongs here rather than math.stackexchange.com $\endgroup$ – Glen_b -Reinstate Monica Mar 16 '13 at 17:40
2
$\begingroup$

Let the state space of the Markov Chain be $S=\{1,2,3,4,5,6\}$. Now draw the state transition diagram.

enter image description here

(a). From the figure, we observe that $\{4\}$, and $\{6\}$ form non-closed communicating classes. State $2$ does not communicate even with itself and such a state is called a non-return state. Hence, the states 2, 4 and 6 are transient.

(b)&(c). The class $\{1,3,5\}$ is a closed-communicating class. Hence, states 1, 3 and 5 are recurrent states.

(c). There is only one closed-communicating class, $\{1,3,5\}$.

(d). As the chain is not an irreducible Markov Chain, it is not an ergodic chain.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.