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References

  1. Barbour, A.D., Brown, T.C. Stein's method and point process approximation. Stochastic Process. Appl. 43 (1992), 9-31. MR1190904
  2. Barbour, A.D., Holst, L., Janson, S. Poisson Approximation. Oxford University Press, Oxford, 1992. MR1163825
  3. Böker, F., Serfozo, R. Ordered thinnings of point processes and random measures. Stochastic Process. Appl. 15 (1983), 113-132. MR0702486
  4. Brown, T.C. Position dependent and stochastic thinning of point processes. Stochastic Process. Appl. 9 (1979), 189-193. MR0548838
  5. Brown, T.C., Weinberg, G.V., Xia, A. Removing logarithms from Poisson process error bounds. Stochastic Process. Appl. 87 (2000), 149-165. MR1751169
  6. Brown, T.C., Xia, A. On metrics in point process approximation. Stochastics Stochastics Rep. 52 (1995), 247-263. MR1381671
  7. Brown, T.C., Xia, A. Stein's method and birth-death processes. Ann. Probab. 29 (2001), 1373-1403. MR1872746
  8. Daley, D.J., Vere-Jones, D. An Introduction to the Theory of Point Processes. Springer, New York, 1988. MR0950166
  9. Doukhan, P. Mixing. Properties and Examples. Lecture Notes in Statistics, 85. Springer, New York, 1994. MR1312160
  10. Dudley, R.M. Real analysis and probability. Wadsworth & Brooks/Cole, Pacific Grove, CA, 1989. MR0982264
  11. Jagers, P., Lindvall, T. Thinning and rare events in point processes. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 28 (1974), 89-98. MR0358978
  12. Kallenberg, O. Limits of compound and thinned point processes. J. Appl. Probability 12 (1975), 269-278. MR0391251
  13. Kallenberg, O. Random Measures, 4th ed. Akademie-Verlag, Berlin; Academic Press, London, 1986. MR0854102
  14. Kallenberg, O. Foundations of Modern Probability, 2nd ed., Springer, New York, 2002. MR1876169
  15. Matheron, G. Random sets and integral geometry. Wiley, New York, 1975. MR0385969
  16. Rényi, A. A characterization of Poisson processes (in Hungarian with summaries in English and Russian). Magyar Tud. Akad. Mat. Kutató Int. Közl. 1 (1957), 519-527. MR0094861
    Translated in Selected papers of Alfréd Rényi, Vol. 1, ed. Pál Turán, Akadémiai Kiadó, Budapest, 1976. MR0421966
  17. Schuhmacher, D. Upper bounds for spatial point process approximations. To appear in Ann. Appl. Probab. 15 (2005), No. 1B. MR number not yet available. Preprint at http://www.math.unizh.ch/~schumi/papers/sppa.pdf
  18. Serfozo, R.F. Compositions, inverses and thinnings of random measures. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 37 (1977), 253-265. MR0423519
  19. Serfozo, R.F. Rarefactions of compound point processes. J. Appl. Probability 21 (1984), 710-719. MR0766809
  20. Stoyan, D., Kendall, W.S., Mecke, J. Stochastic geometry and its applications. Wiley, Chichester, 1987. MR0895588
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