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Modelling log Gaussian Cox processes with a given reliability and accuracy

Author(s): Yu. V. Kozachenko; O. O. Pogorilyak
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 76 (2007).
Journal: Theor. Probability and Math. Statist. No. 76 (2008), 77-91.
MSC (2000): Primary 68U20; Secondary 60G10
Posted: July 14, 2008
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Abstract: We consider stochastic Cox processes governed by a random intensity. Namely we consider the case where the logarithm of intensity is a separable stationary Gaussian stochastic process. We construct models approximating log Gaussian Cox processes with a given reliability and accuracy.

References:

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A. Brix and J. Møller, Space-time multi-type log Gaussian Cox processes with a view to modelling weeds, Scand. J. Statist. 28 (2001), no. 3, 471-488.

MR 1858412 (2002g:60072)

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J. Møller, A. R. Syversveen, and R. P. Waagepetersen, Log Gaussian Cox processes, Scand. J. Statist. 25 (1998), no. 3, 451-482.

MR 1650019 (2000k:62156)

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V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, American Mathematical Society, Providence, Rhode Island, 2000. MR 1743716 (2001g:60089)

4.
Yu. V. Kozachenko and A. O. Pashko, Modelling Stochastic Processes, ``Kyiv University'', Kyiv, 1999. (Ukrainian)

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Additional Information:

Yu. V. Kozachenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: yvk@univ.kiev.ua

O. O. Pogorilyak
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: alex_pogorilyak@ukr.net

DOI: 10.1090/S0094-9000-08-00733-3
PII: S 0094-9000(08)00733-3
Keywords: Log Gaussian Cox processes, random intensity, modelling, accuracy, reliability
Received by editor(s): 23/FEB/2006
Posted: July 14, 2008
Copyright of article: Copyright 2008, American Mathematical Society

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