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  • Central limit theorems for functionals of stationary germ-grain models

  • Part of
  • Ursa Pantle, Volker Schmidt, Evgueni Spodarev
  • Journal:
    Advances in Applied Probability / Volume 38 / Issue 1 / March 2006
    Published online by Cambridge University Press:
    01 July 2016, pp. 76-94
    Print publication:
    March 2006
    • Article
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  • Conditions are derived for the asymptotic normality of a general class of vector-valued functionals of stationary Boolean models in the d-dimensional Euclidean space, where a Lindeberg-type central limit theorem for m-dependent random fields, m ∈ N, is applied. These functionals can be used to construct joint estimators for the vector of specific intrinsic volumes of the underlying Boolean model. Extensions to functionals of more general germ–grain models satisfying some mixing and integrability conditions are also discussed.