Question: 6.6.1 Let Yn;n D 0;1; : : : ; be a discrete time Markov chain with transition probabilities P D kPijk, and let fN.t/I t

6.6.1 Let Yn;n D 0;1; : : : ; be a discrete time Markov chain with transition probabilities P D kPijk, and let fN.t/I t 0g be an independent Poisson process of rate .

Argue that the compound process X.t/ D YN.t/; t 0;

is a Markov chain in continuous time and determine its infinitesimal parameters.

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