A Parameter Estimation Procedure for a Partially Observed Replacement Problem

We present, for a partially observed Markovian replacement problem, a recursive parameter estimation algorithm that can take into account an arbitrary (random) number of observations made in each regenerative cycle. The algorithm updates the parameter estimate only after replacement times. Convergence with probability one (w.p.1) is established by using the `ordinary differential equation´ (ODE) method. Rates of convergence and asymptotic relative efficiencies are considered by means of a diffusion approximation procedure.