Moment measures of mixed empirical random point processes and marked point processes in compact metric spaces. I
Author:
M. G. Semeĭko
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 88 (2014), 161-174
MSC (2010):
Primary 60G55
DOI:
https://doi.org/10.1090/S0094-9000-2014-00926-6
Published electronically:
July 24, 2014
MathSciNet review:
3112642
Full-text PDF Free Access
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Additional Information
Abstract: Moment measures of mixed empirical random point processes and marked point processes are investigated by using probability generating functions of random counting measures.
References
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References
- N. G. Semeĭko, Yu. I. Petunin, and V. P. Yatsenko, Studying the morphometric characteristics of nuclear pore complexes of a sensory neuron using methods of spherical stochastic geometry, Kibernetika and Sistemnyi Analiz 42 (2006), no. 6, 175–182; English transl. in Cybernetics and Systems Analysis 42 (2006), no. 6, 917–922.
- A. Baddeley and E. B. Vedel Jensen, Stereology for Statisticians, Chapman and Hall/CRC, New York, 2005. MR 2107000 (2005g:62001)
- G. S. Watson, Mathematical morfology, A Survey of Statistical Design and Linear Models (I. N. Srivastava, ed.), North-Holland Publishing Company, 1975, pp. 547–553. MR 0378323 (51:14491)
- A. F. Karr, Point Processes and Their Statistical Inference, Marcel Dekker, New York, 1991. MR 1113698 (92f:62116)
- M. Csörgő and P. Révész, Strong Approximation in Probability and Statistics, Academic Press, New York, 1981. MR 666546 (84d:60050)
- P. Gaenssler, Empirical Processes: On Some Basic Results from the Probabilistic Point of View, Institute of Mathematical Statistics, Hayward, CA, 1984.
- P. Gaenssler and W. Stute, On uniform convergence of measures with application to uniform convergence of empirical distribution, Lect. Notes Math., vol. 566, 1976, pp. 45–56. MR 0433534 (55:6510)
- D. Pollard, Convergence of Stochastic Processes, Springer-Verlag, New York, 1984. MR 762984 (86i:60074)
- R. Serfling, Approximation Theorems of Mathematical Statistics, Wiley, New York, 1980. MR 595165 (82a:62003)
- Yu. I. Petunin and M. G. Semeĭko, Mixed empirical stochastic point processes in compact metric spaces. I, Teor. Imovir. Mat. Stat. 74 (2006), 98–107; English transl. in Theory Probab. Math. Statist. 74 (2007), 113–123. MR 2321193 (2008f:60053)
- Yu. I. Petunin and M. G. Semeĭko, Mixed empirical stochastic point processes in compact metric spaces. II, Teor. Imovir. Mat. Stat. 75 (2006), 121–126; English transl. in Theory Probab. Math. Statist. 74 (2007), 139–145. MR 2321187 (2008f:60054)
- N. G. Semeĭko, Mixed empirical Poisson random spherical-cap process, Kibernetika ta sistemnyi analiz (2011), no. 5, 119–130; English transl. in Cybernetics and Systems Analysis 47 (2011), no. 5, 773–782.
- J. E. Moyal, The general theory of stochastic population processes, Acta Math. 108 (1962), no. 1, 1–31. MR 0148107 (26:5616)
- B. D. Ripley, Locally finite random sets: foundations for point process theory, Ann. Probab. 4 (1976), no. 6, 983–994. MR 0474478 (57:14117)
- K. Matthes, J. Kerstan, and J. Mecke, Infinitely Divisible Point Processes, John Wiley & Sons, Chichester–New York–Brisbane–Toronto 1978. MR 0517931 (58:24538)
- O. Kallenberg, Random Measures, Akademie-Verlag, Berlin, 1975. MR 0431372 (55:4372)
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Additional Information
M. G. Semeĭko
Affiliation:
Department of Higher Mathematics, Faculty for Human Resources Management and Marketing, Kyiv National Vadym Get’man University for Economics, Peremogy Avenue, 54/1, Kyiv 03680, Ukraine
Email:
semejko@ukr.net
Keywords:
Mixed empirical point processes,
marked point processes,
probability generating functions,
moment measures
Received by editor(s):
September 15, 2011
Published electronically:
July 24, 2014
Article copyright:
© Copyright 2014
American Mathematical Society