#6 (Chapter 4, Exercise 37) Show that the stationary probabilities for the Markov chain having transition probabilities Pij are also the stationary probabilities for the Markov chain whose transition probabilities Qij are given by Qi.j = Pij for any specified positive integer k.

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#6 (Chapter 4, Exercise 37) Show that the stationary probabilities for the Markov
chain having transition probabilities Pij are also the stationary probabilities for the Markov
chain whose transition probabilities Qij are given by
Qij = Ph
for any specified positive integer k.
Text book answer
7. Must show that
#j = {^;Plj
πi
i
The preceding follows because the right-hand side
is equal to the probability that the Markov chain
with transition probabilities P₁,¡ will be in state j
at time k when its initial state is chosen according
to its stationary probabilities, which is equal to its
stationary probability of being in state j.
I need a more
specific proceeding of the answer,
Transcribed Image Text:#6 (Chapter 4, Exercise 37) Show that the stationary probabilities for the Markov chain having transition probabilities Pij are also the stationary probabilities for the Markov chain whose transition probabilities Qij are given by Qij = Ph for any specified positive integer k. Text book answer 7. Must show that #j = {^;Plj πi i The preceding follows because the right-hand side is equal to the probability that the Markov chain with transition probabilities P₁,¡ will be in state j at time k when its initial state is chosen according to its stationary probabilities, which is equal to its stationary probability of being in state j. I need a more specific proceeding of the answer,
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