A NOTE ON IMPORTANCE SAMPLING SIMULATION FOR A
GERM-GRAIN MODEL
Abstract: In this paper we demonstrate how to use the importance sampling method to
simulate rare events in a germ-grain model. We analyze conditions under which two
germ-grain models are mutually absolutely continuous. We also find the likelihood set
process. We apply these results in simulating the probability that the radius of the occupied
component of the origin in continuous percolation is greater than some This method is
based on the reduction of the variance of estimator.
2000 AMS Mathematics Subject Classification: Primary 60D05, 62M05; Secondary
60K35, 82B43, 62M30.
Key words and phrases: Germ-grain model, Poisson process, change of measure,
likelihood process, stopping set.