Modelling log Gaussian Cox processes with a given reliability and accuracy. (Ukrainian, English) Zbl 1199.60115

Kozachenko, Yu. V.; Pogorilyak, O. O.

Teor. Jmovirn. Mat. Stat. 76, 70-83 (2007); translation in Theory Probab. Math. Stat. 76, 77-91 (2008).

The authors propose a method of construction of models for the so-called doubly stochastic Poisson processes or, in other words, Cox processes governed by a random intensity. The case where the intensity is a log Gaussian stochastic process is considered. Log Gaussian Cox processes and their models are studied in the papers [A. Brix and J. Møller, Scand. J. Stat. 28, No. 3, 471–488 (2001; Zbl 0981.62079); J. Møller, A. R. Syversveen and R. P. Waagepetersen, Scand. J. Stat. 25, No. 3, 451–482 (1998; Zbl 0931.60038)] for the case where the intensity is a random field. In contrast to the results of these papers, the authors of the paper under review propose an approach to model stochastic processes with a given reliability and accuracy. The problem of choosing a partition used in the modeling is discussed. The model itself is constructed. Sufficient conditions for the approximation with a given reliability and accuracy are given.
For more results and references see the book by Yu. V. Kozachenko, A. O. Pashko and I. V. Rozora [Modelling of random processes and fields, Kyïv: Zadruga (2007; Zbl 1199.60003)].

Reviewer: Mikhail P. Moklyachuk (Kyïv)

MSC:

60G10	Stationary stochastic processes
65C50	Other computational problems in probability (MSC2010)

Keywords:

stochastic Cox process; stationary Gaussian stochastic process; approximation; log Gaussian Cox process; reliability; accuracy

Citations:

Zbl 0981.62079; Zbl 0931.60038; Zbl 1199.60003