Mixed empirical point random processes in compact metric spaces. II
Authors:
Yu. I. Petunin and M. G. Semeĭko
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 75 (2007), 139-145
MSC (2000):
Primary 60G55
DOI:
https://doi.org/10.1090/S0094-9000-08-00720-5
Published electronically:
January 24, 2008
MathSciNet review:
2321187
Full-text PDF Free Access
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Abstract: Models of finite simple mixed empirical ordered marked point processes in compact metric spaces are studied in the paper. The processes are constructed from simple samples drawn without replacement from a population. The notion of an ordered marked point process with independent and 1-dependent marks is introduced. Examples of ordered marked point processes with independent and 1-dependent marks are given.
References
- Yu. I. Petunin and N. G. Semeĭko, A random process of segments on a two-dimensional Euclidean sphere. I, Teor. Veroyatnost. i Mat. Statist. 39 (1988), 107–113, 128 (Russian); English transl., Theory Probab. Math. Statist. 39 (1989), 129–135. MR 947940, DOI https://doi.org/10.1090/s0094-9000-07-00701-6
- Alan F. Karr, Point processes and their statistical inference, 2nd ed., Probability: Pure and Applied, vol. 7, Marcel Dekker, Inc., New York, 1991. MR 1113698
- Günter Last and Andreas Brandt, Marked point processes on the real line, Probability and its Applications (New York), Springer-Verlag, New York, 1995. The dynamic approach. MR 1353912
- Yu. I. Petunin and N. G. Semeĭko, Random cap process and generalized Wicksell problem on the surface of a sphere, Serdica 17 (1991), no. 2-3, 81–91 (1992). MR 1148300
- András Prékopa, On secondary processes generated by a random point distribution of Poisson type, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 1 (1958), 153–170. MR 119243
- D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic geometry and its applications, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons, Ltd., Chichester, 1987. With a foreword by D. G. Kendall. MR 895588
- Yu. Ī. Petunīn and M. G. Semeĭko, Mixed empirical random point processes in compact metric spaces. I, Teor. Ĭmovīr. Mat. Stat. 74 (2006), 98–107 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 74 (2007), 113–123. MR 2321193, DOI https://doi.org/10.1090/S0094-9000-07-00701-6
References
- Yu. I. Petunin and N. G. Semeĭko, A random process of segments on a two-dimensional Euclidean sphere. I, Teor. Veroyatnost. i Mat. Statist. 39 (1988), 107–113; English transl. in Theory Probab. Math. Statist. 39 (1989), 129–135. MR 947940 (89g:60170)
- A. F. Karr, Point Processes and their Statistical Inference, 2nd ed., Marcel Dekker, New York, 1991. MR 1113698 (92f:62116)
- G. Last and A. Brandt, Marked Point Processes on the Real Line: the Dynamic Approach, Springer-Verlag, New York, 1995. MR 1353912 (97c:60126)
- Yu. I. Petunin and N. G. Semeĭko, Random cap process and generalized Wickell problem on the surface of a sphere, Serdica 17 (1991), 81–91. MR 1148300 (93c:60010)
- A. Prekopa, On secondary processes generated by a random point distribution of Poisson type, Ann. Univ. Sci. Budapest. Eötvös. Sect. Math 1 (1958), 153–170. MR 0119243 (22:10009)
- D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and its Application, 2nd ed., John Wiley & Sons, New York, 1987. MR 895588 (88j:60034a)
- Yu. I. Petunin and N. G. Semeĭko, Mixed empirical stochastic point processes in compact metric spaces. I, Teor. Imovirnost. ta Mat. Statist. 74 (2006), 99–109; English transl. in Theory Probab. Math. Statist. 74 (2007), 113–123. MR 2321193
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Additional Information
Yu. I. Petunin
Affiliation:
Faculty for Cybernetics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email:
vm214@dcp.kiev.ua
M. G. Semeĭko
Affiliation:
Department of Higher Mathematics, Kyiv National University for Economy, Peremogy Avenue, 54/1, Kyiv, 03057, Ukraine
Email:
semejko@ukr.net
Received by editor(s):
April 13, 2005
Published electronically:
January 24, 2008
Article copyright:
© Copyright 2008
American Mathematical Society
