Central limit theorems for functionals of stationary germ-grain models

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 co...

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Bibliographic Details
Published in:Advances in applied probability 2006-03, Vol.38 (1), p.76-94
Main Authors: Pantle, Ursa, Schmidt, Volker, Spodarev, Evgueni
Format: Article
Language:English
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Summary: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.
ISSN:0001-8678
1475-6064
DOI:10.1017/S0001867800000811