4. Consider the Markov chain shown in below figure. It is assumed that when there is an arrow from state i to state j, then $p_{ij} > 0$. Find the equivalence classes for this Markov chain. Which class is recurrent? Which class is transient? Calculate the period of each class.
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From the diagram, we can see the following transitions: - State 1: can go to state 2 - State 2: can go to state 1 and 3 - State 3: can go to state 4 and 2 - State 4: can go to state 5 and 3 - State 5: can go to state 4 and 6 - State 6: can go to state 5 and 7 - Show more…
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Specify the classes of the following Markov chains, and determine whether they are transient or recurrent: $$ \begin{aligned} &\mathbf{P}_{1}=\left|\begin{array}{ccc} 0 & \frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & 0 & \frac{1}{2} \\ \frac{1}{2} & \frac{1}{2} & 0 \end{array} \| \quad \mathbf{P}_{2}=\right| \begin{array}{llll} 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 \\ \frac{1}{2} & \frac{1}{2} & 0 & 0 \\ 0 & 0 & 1 & 0 \end{array} \mid\\ &\mathbf{P}_{3}=\left|\begin{array}{ccccc} \frac{1}{2} & 0 & \frac{1}{2} & 0 & 0 \\ \frac{1}{4} & \frac{1}{2} & \frac{1}{4} & 0 & 0 \\ \frac{1}{2} & 0 & \frac{1}{2} & 0 & 0 \\ 0 & 0 & 0 & \frac{1}{2} & \frac{1}{2} \\ 0 & 0 & 0 & \frac{1}{2} & \frac{1}{2} \end{array}\left\|\quad \mathbf{P}_{4}=\mid \begin{array}{lllll} \frac{1}{2} & 4 & 0 & 0 & 0 \\ \frac{1}{2} & \frac{1}{2} & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & + & - & 0 \\ 1 & 0 & 0 & 0 & 0 \end{array}\right\|\right. \end{aligned} $$
Aarti K.
Breanna O.
Consider the Markov chain whose transition probability matrix is: P = ( 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1/3 1/3 1/3 0 0 1 0 0 0 0 0 1/2 0 0 0 1/2 ) a) Classify the states {0, 1, 2, 3, 4, 5} into classes. (b) Identify the recurrent and transient classes of (a).
Ameer S.
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