A note on impotance sampling simulation for germ-grain model

• Autorzy: Palmowski Z.
• Języki publikacji: EN

Abstrakty

EN

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 R. This method is based on the reduction of the variance of estimator.

Słowa kluczowe

EN

germ-grain model; Poisson process; change of measure; likelihood process; stopping set

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2003
• Tom: Vol. 23, Fasc. 2
• Strony: 293--304
• Opis fizyczny: Bibliogr. 8 poz., tab.

Twórcy

autor

Palmowski Z.

• Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] S. Asmussen, Stochastic Simulation with a View towards Stochastic Processes, MaPhySto Lecture Notes No 2, University of Aarhus, 1999.
• [2] G. Grimmett, Percolation, Springer, Berlin 1999.
• [3] J. Jacod, Multivariate point processes: Predictable projection, Radon-Nikodym derivatives, representation of martingales, Z. Wahrsch. verw. Gebiete 31 (1975), pp. 235-253.
• [4] A. F. Karr, Point Processes and Their Statistical Inference, 2nd edition, Probability: Pure and Applied, New York 1991.
• [5] G. Matheron, Random Sets and Integral Geometry, Wiley, Chichester 1975.
• [6] K. Matthes, J. Kerstan and J. Mecke, Infinitely Divisible Point Processes, Wiley, Chichester 1978.
• [7] R. Meester and R. Roy, Continuum Percolation, Cambridge University Press, Cambridge 1996.
• [8] M. N. M. Van Lieshout, Stochastic Geometry Models in Image Analysis and Spatial Statistics, CWI Tracts, Amsterdam 1995.