Show that all states of embedded markov chain are transient

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Reference no: EM13909089

(a) Consider a Markov process with the set of states {0, 1, .. .} in which the transition rates {qij} between states are given by qi,i+1 = (3/5)2i for i ≥ 0, qi,i-1 = (2/5)2i for i ≥ 1, and qij = 0 otherwise. Find the transition rate νi out of state ifor each i ≥ 0 and find the transition probabilities {Pij} for the embedded Markov chain.

(b) Find a solution {pi; i ≥ 0} with J,i pi = 1 to (7.23).

(c) Show that all states of the embedded Markov chain are transient.

(d) Explain in your own words why your solution to (b) is not in any sense a set of steady-state probabilities.

Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.

Reference no: EM13909089

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