Stochastic modelling and statistics of polymer crystallization process

Crystallization of polymers is modelled as a spatially structured process consisting of a nucleation phase and a growth phase. A counting process approach together with methods of stochastic geometry leads us to the evolution equations of the relevant quantities of the process. In particular we provide local and global convergence of the stochastic growth process to its expected value, thus justifying the use of deterministic models to predict the results of real experiments. Estimates of the relevant parameters of the process are obtained via the maximum likelihood method, and also by a nonparametric method based on the estimation of the hitting function of the associated Boolean model. Asymptotic properties of the estimators are given and computer experiments are reported to show their qualitative behaviour, as a function of the available volume and of time.