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Mixed empirical point random processes in compact metric spaces. II
Author(s):
Yu.
I.
Petunin;
M.
G.
Semeiko
Translated by:
N. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 75
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 75
(2007),
139-145.
MSC (2000):
Primary 60G55
Posted:
January 24, 2008
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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:
-
- 1.
- 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)
- 2.
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- 3.
- G. Last and A. Brandt, Marked Point Processes on the Real Line: the Dynamic Approach, Springer-Verlag, New York, 1995. MR 1353912 (97c:60126)
- 4.
- 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)
- 5.
- 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)
- 6.
- 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)
- 7.
- 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.
Semeiko
Affiliation:
Department of Higher Mathematics, Kyiv National University for Economy, Peremogy Avenue, 54/1, Kyiv, 03057, Ukraine
Email:
semejko@ukr.net
DOI:
10.1090/S0094-9000-08-00720-5
PII:
S 0094-9000(08)00720-5
Received by editor(s):
13/APR/2005
Posted:
January 24, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
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