With P denoting the transition matrix defined in Exercise 10.9 of Chapter 2, let Q = P - I and consider a continuous time jump Markov process {Xt; t ≥ 0} whose infinitesimal generator is Q. 1. Give the transition matrix P of the embedded chain.
1. Give the transition matrix P of the embedded chain.
2. Describe the trajectories of the process {Xt}, and specify the parameters of the exponential laws of the time spent in the various states.
3. Show that the process {Xt} is irreducible and positive recurrent. Determine its invariant probability distribution.
4. Determine the invariant probability distribution of the embedded chain