Letnbspn1t tnbspge 0 be a homogeneous poisson process with

Question

Let {N₁(t) t ≥ 0} be a (homogeneous) Poisson process with rate λ = 1, and let {N₂(t),t ≥ 0} be a nonhomogeneous Poisson process whose intensity function is

We suppose that the two stochastic processes are independent. Moreover, let {Y(t) t ≥ 0} be a compound Poisson process defined by