International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2002 / Article

Open Access

Volume 15 |Article ID 207018 | https://doi.org/10.1155/S1048953302000254

Marcello De Giosa, Rosa Maria Mininni, "Free area estimation in a partially observed dynamic germ-grain model", International Journal of Stochastic Analysis, vol. 15, Article ID 207018, 21 pages, 2002. https://doi.org/10.1155/S1048953302000254

Free area estimation in a partially observed dynamic germ-grain model

Received01 Apr 2001
Revised01 Mar 2002

Abstract

The estimation problem of the expected local fraction of free area function S for a partially observed dynamic germ-grain model is presented. Properties of the estimators are proved by martingale and product integral methods. Confidence bounds are provided. Furthermore, an estimator of the hazard rate α(t)=dS(t)/(S(t)dt) is obtained by the kernel function method and asymptotic properties of the estimator are proved and used to find confidence intervals. By a simulated illustrative example, the qualitative behavior of the estimators is shown.

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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