Compound Poisson Processes. Let X(t) denote a compound Poisson process as in Section 3.15 in Chapter 3 with rate λ and jump-size density f(i), i ∈ Z. Justify that X(t) is a CTMC and specify its...

Compound Poisson Processes. Let X(t) denote a compound Poisson process as in Section 3.15 in Chapter 3 with rate λ and jump-size density f(i), i ∈ Z. Justify that X(t) is a CTMC and specify its transition rates. Assuming X(t) is irreducible on Z, classify its states when the mean of the density f is = 0 or is = 0.