Estimation Problems for a Crystallization Process Modelled by a Dynamic Germ-Grain Model

A random dynamic germ-grain model Θ(t), t ≥ 0, in ℝ2 is studied and a product limit type estimator of the free volume fraction S(t) = P(0 ∉ Θ(t)) is proposed. A kernel function estimator of a parameter a involved in S is also suggested. Both the estimators satisfy Consistence and Asymptotic Normality properties. Confidence bands and intervals are provided. Numerical simulations of the model have been carried out to show the qualitative behaviour of the estimators.