Could you explain how to find the Poisson Process and the discrete time Markov chain such that we can write the representation Y(t) = X_N(t)?

Consider the continuous time Markov chain {Y (t) : t Z 0} living in the state space {1, 2, 3, 4} with generator matrix Find a Poisson process N( ') (specify the rate 7L of the process) and a discrete time Markov chain (X11: n 2 0) (specify the transition matrix of this Markov chain) such that we can write the representation Y(t) = XN(:)