Journal of Applied Mathematics and Stochastic Analysis 
Volume 2006 (2006), Article ID 50786, 14 pages
doi:10.1155/JAMSA/2006/50786

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

Abstract

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.