Question
Let {X(t)} be a continuous-time Markov chain with stationary distribution. We sample the chain at times given by an independent Poisson process: let N(t)
Let {X(t)} be a continuous-time Markov chain with stationary distribution. We sample the chain at times given by an independent Poisson process: let N(t) be a Poisson process with rate a, independent of the Markov chain, and define Y, = X(T +), the value taken by X immediately after the epoch T, of the nth arrival of N. Show that {Y} is a discrete-time Markov chain with the same stationary distribution as X.
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Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers
Authors: Roy D. Yates, David J. Goodman
3rd edition
1118324560, 978-1118324561
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