Consider a nonhomogeneous Poisson process whose intensity function λ(t) is bounded and continuous. Show that such a process is equivalent to a process of counted events from a (homogeneous) Poisson...

Consider a nonhomogeneous Poisson process whose intensity function λ(t) is bounded and continuous. Show that such a process is equivalent to a process of counted events from a (homogeneous) Poisson process having rate λ, where an event at time t is counted (independent of the past) with probability λ(t)/λ; and where λ is chosen so that λ(s) ≤ for all s.