The estimation problem of the expected local fraction of free area function S for a
partially observed dynamic germ-grain model is presented. Properties of the
estimators are proved by martingale and product integral methods. Confidence
bounds are provided. Furthermore, an estimator of the hazard rate
α(t)=−dS(t)/(S(t)dt)
is obtained by the kernel function method and
asymptotic properties of the estimator are proved and used to find confidence
intervals. By a simulated illustrative example, the qualitative behavior of the
estimators is shown.