Recursive approximate maximum likelihood estimation for a class of counting process models

In this paper we present a recursive algorithm that produces estimators of an unknown parameter that occurs in the intensity of a counting process. The estimators can be considered as approximations of the maximum likelihood estimator. We prove consistency of the estimators and derive their asymptotic distribution by using Lyapunov functions and weak convergence for martingales. The conditions that we impose in order to prove our results are similar to those in papers on (quasi) least squares estimation.