Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 50786, 14 pages

Free area estimation in a dynamic germ-grain model with renewal dropping process

Marcello De Giosa

Dipartimento di Matematica, Università di Bari, Via Orabona 4, Bari 70125, Italy

Received 20 December 2004; Revised 8 April 2005; Accepted 30 April 2005

Copyright © 2006 Marcello De Giosa. 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.


A partially observed dynamic germ-grain model with renewal dropping process is considered. The expected fraction of free area function is estimated by a product integral-type estimator. Uniform consistency and asymptotic Gaussianity of the estimator are proved. Confidence bands and simulation results are also provided.