UNSPECIFIED (1999) Perfect simulation in stochastic geometry. PATTERN RECOGNITION, 32 (9). pp. 1569-1586. ISSN 0031-3203

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Abstract

Simulation plays an important role in stochastic geometry and related fields, because all but the simplest random set models tend to be intractable to analysis. Many simulation algorithms deliver (approximate) samples of such random set models, for example by simulating the equilibrium distribution of a Markov chain such as a spatial birth-and-death process. The samples usually fail to be exact because the algorithm simulates the Markov chain for a long but finite time, and thus convergence to equilibrium is only approximate. The seminal work by Propp and Wilson made an important contribution to simulation by proposing a coupling method, coupling from the past (CFTP), which delivers perfect, that is to say exact, simulations of Markov chains. In this paper we introduce this new idea of perfect simulation and illustrate it using two common models in stochastic geometry: the dead leaves model and a Boolean model conditioned to cover a finite set of points. (C) 1999 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software T Technology > TK Electrical engineering. Electronics Nuclear engineering
Journal or Publication Title:	PATTERN RECOGNITION
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
ISSN:	0031-3203
Date:	September 1999
Volume:	32
Number:	9
Number of Pages:	18
Page Range:	pp. 1569-1586
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/14406

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