COMPENSATOR CONDITIONS FOR STOCHASTIC ORDERING OF POINT-PROCESSES

Sufficient conditions are given under which two simple point processes on the positive half-line can be stochastically compared as random elements of D(0, infinity) or R+ infinity. Using a martingale approach to point processes, the conditions are proposed via a compensator function family. Appropriate versions of the processes being compared are constructed on the same probability space. The results are illustrated by replacement policies and semi-Markov point processes.