Strong consistency of sample path derivative estimates

Easily verified conditions for strong consistency of infinitesimal perturbation analysis (IPA) derivative estimates for discrete-event systems are established. Modeling the system as a generalized semi-Markov process (GSMP), one can formulate the IPA derivative estimate as a reward functional on an augmented process which is defined on the original GSMP. Conditions are given under which regeneration of the GSMP implies regeneration of this augmented process. Standard moment assumptions (on the GSMP) along with other easily checked conditions then imply strong consistency.<>