*45. Consider a nonhomogeneous Poisson process whose intensity function () is bounded and continuous. Show that such...

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