Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

Request Permissions   Purchase Content 
 
 

 

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
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 88 (2013).
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

Abstract | References | Similar Articles | 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 [Enhancements On Off] (What's this?)

  • 1. 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.
  • 2. A. Baddeley and E. B. Vedel Jensen, Stereology for Statisticians, Chapman and Hall/CRC, New York, 2005. MR 2107000 (2005g:62001)
  • 3. 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)
  • 4. A. F. Karr, Point Processes and Their Statistical Inference, Marcel Dekker, New York, 1991. MR 1113698 (92f:62116)
  • 5. M. Csörgő and P. Révész, Strong Approximation in Probability and Statistics, Academic Press, New York, 1981. MR 666546 (84d:60050)
  • 6. P. Gaenssler, Empirical Processes: On Some Basic Results from the Probabilistic Point of View, Institute of Mathematical Statistics, Hayward, CA, 1984.
  • 7. 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)
  • 8. D. Pollard, Convergence of Stochastic Processes, Springer-Verlag, New York, 1984. MR 762984 (86i:60074)
  • 9. R. Serfling, Approximation Theorems of Mathematical Statistics, Wiley, New York, 1980. MR 595165 (82a:62003)
  • 10. 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)
  • 11. 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)
  • 12. 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.
  • 13. J. E. Moyal, The general theory of stochastic population processes, Acta Math. 108 (1962), no. 1, 1-31. MR 0148107 (26:5616)
  • 14. B. D. Ripley, Locally finite random sets: foundations for point process theory, Ann. Probab. 4 (1976), no. 6, 983-994. MR 0474478 (57:14117)
  • 15. K. Matthes, J. Kerstan, and J. Mecke, Infinitely Divisible Point Processes, John Wiley & Sons, Chichester-New York-Brisbane-Toronto 1978. MR 0517931 (58:24538)
  • 16. O. Kallenberg, Random Measures, Akademie-Verlag, Berlin, 1975. MR 0431372 (55:4372)
  • 17. P. I. Daley, Various concepts of orderliness for point processes, Stochastic Geometry (R. F. Harding and P. G. Kendall, eds.), New York, 1974, pp. 148-164. MR 0380976 (52:1873)
  • 18. G. Birkhoff, Lattice Theory, American Mathematical Society Colloquium Publications, vol. 25, revised edition, American Mathematical Society, New York, 1948. MR 0029876 (10:673a)
  • 19. Yu. I. Petunin and N. G. Semeĭko, A random process of segments on a two-dimensional Euclidean sphere I, Teor. Veroyatnost. Mat. Statist. 39 (1988), 107-113; English transl. in Theory Probab. Math. Statist. 39 (1989), 129-135. MR 947940 (89g:60170)
  • 20. P. Gaenssler, Empirical Processes, Lecture Notes, Regional Monograph Series, vol. 2, Institute of Mathematical Statistics, Munich, 1983. MR 744668 (86f:60044)
  • 21. D. I. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes, Springer-Verlag, New York, 1988. MR 950166 (90e:60060)
  • 22. R L. Bishop and R. J. Crittenden, Geometry of Manifolds, Academic Press, New York, 1964. MR 0169148 (29:6401)
  • 23. Hassler Whitney, Geometric Integration Theory, Princeton University Press, Princeton, 1957. MR 0087148 (19:309c)
  • 24. V. S. Koroljuk, N. I. Portenko, A. V. Skorohod, and A. F. Turbin, A Manual on Probability Theory and Mathematical Statistics, ``Naukova Dumka'', Kiev, 1978. (Russian) MR 502722 (80b:60002)
  • 25. W. Feller, An Introduction to Probability Theory and Its Applications, vol. 1, Wiley, New York, 1950. MR 0038583 (12:424a)
  • 26. N. A. J. Hastings and J. B. Peacock, Statistical Distributions: A Handbook for Students and Practitioners, Butterworth, London, 1975. MR 0359137 (50:11592)

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60G55

Retrieve articles in all journals with MSC (2010): 60G55


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

DOI: https://doi.org/10.1090/S0094-9000-2014-00926-6
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

American Mathematical Society