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

  • M. De Giosa
  • R. M. Mininni
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 1)


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.


Asymptotic Normality Unbiased Estimator Confidence Band Boolean Model Functional Central Limit Theorem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • M. De Giosa
    • 1
  • R. M. Mininni
    • 1
  1. 1.Dipartimento di MatematicaUniversità di BariBariItaly

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