Modelling log Gaussian Cox processes with a given reliability and accuracy
Authors:
Yu. V. Kozachenko and O. O. Pogorilyak
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 76 (2008), 77-91
MSC (2000):
Primary 68U20; Secondary 60G10
DOI:
https://doi.org/10.1090/S0094-9000-08-00733-3
Published electronically:
July 14, 2008
MathSciNet review:
2368741
Full-text PDF Free Access
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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
- Anders Brix and Jesper 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, DOI https://doi.org/10.1111/1467-9469.00249
- Jesper Møller, Anne Randi Syversveen, and Rasmus Plenge Waagepetersen, Log Gaussian Cox processes, Scand. J. Statist. 25 (1998), no. 3, 451–482. MR 1650019, DOI https://doi.org/10.1111/1467-9469.00115
- V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, Translations of Mathematical Monographs, vol. 188, American Mathematical Society, Providence, RI, 2000. Translated from the 1998 Russian original by V. Zaiats. MR 1743716
- Yu. V. Kozachenko and A. O. Pashko, Modelling Stochastic Processes, “Kyiv University”, Kyiv, 1999. (Ukrainian)
References
- 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)
- 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)
- 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)
- 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
Keywords:
Log Gaussian Cox processes,
random intensity,
modelling,
accuracy,
reliability
Received by editor(s):
February 23, 2006
Published electronically:
July 14, 2008
Article copyright:
© Copyright 2008
American Mathematical Society
