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1. Consider a continuous-time Markov chain with no absorbing states. Let G be its generator matrix and R the transition matrix of its jump chain.

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1. Consider a continuous-time Markov chain with no absorbing states. Let G be its generator matrix and R the transition matrix of its jump chain. Let x = (:12; : i E S) be a row vector of nonnegative values, and let 3; = (yi : i E S) be given by y; = migi, where g,- = g,;,i. (a) Show that $6 = 0 if and only if yR = y. (b) Explain briey why this result is natural in the case when both chains are positive recurrent

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