A Markov chain has state space ( mathbf Z 0,1,2,3,4 ) and transition matrix mathbf P left( begin array ccccc 0 5 0 1 0 4 0 0 0 8 0 2 0 0 0 0 1 0 0 0 0 0 0 0 9 0 1 0 0 0 1 0 end array ight) (1) Determine the minimal closed sets (2) Identify essential and inessential states (3) What are the recurrent...

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A Markov chain has state space (mathbf{Z}={0,1,2,3,4}) and transition matrix [mathbf{P}=left(begin{array}{ccccc} 0.5 & 0.1 & 0.4 &

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A Markov chain has state space $\mathbf{Z}=\{0,1,2,3,4\}$ and transition matrix

\[\mathbf{P}=\left(\begin{array}{ccccc} 0.5 & 0.1 & 0.4 & 0 & 0 \\ 0.8 & 0.2 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0.9 & 0.1 \\ 0 & 0 & 0 & 1 & 0 \end{array}\right)\]

(1) Determine the minimal closed sets.

(2) Identify essential and inessential states.

(3) What are the recurrent and transient states?

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Applied Probability And Stochastic Processes

ISBN: 9780367658496

2nd Edition

Authors: Frank Beichelt

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Question Posted: Apr 26, 2024 04:01 PM

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A Markov chain has state space (mathbf{Z}={0,1,2,3,4}) and transition matrix [mathbf{P}=left(begin{array}{ccccc} 0.5 & 0.1 & 0.4 &

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Applied Probability And Stochastic Processes

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