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References

  1. Barbour, A. D. Stein's method and Poisson process convergence.A celebration of applied probability. J. Appl. Probab. 1988, Special Vol. 25A, 175--184. MR0974580 (90a:60064)
  2. Barbour, A. D.; Jensen, J. L. Local and tail approximations near the Poisson limit. Scand. J. Statist. 16 (1989), no. 1, 75--87. MR1003970 (91a:60057)
  3. Barbour, A. D.; Xia, A. The number of two-dimensional maxima. Adv. in Appl. Probab. 33 (2001), no. 4, 727--750. MR1875775 (2002j:60016)
  4. Barbour, A. D.; \v Cekanavi\v cius, V. Total variation asymptotics for sums of independent integer random variables. Ann. Probab. 30 (2002), no. 2, 509--545. MR1905850 (2003g:60072)
  5. Barbour, Andrew D.; Xia, Aihua. Poisson perturbations. ESAIM Probab. Statist. 3 (1999), 131--150 (electronic). MR1716120 (2000j:60026)
  6. Barbour, A. D.; Karo\'nski, Micha\l; Ruci\'nski, Andrzej. A central limit theorem for decomposable random variables with applications to random graphs. J. Combin. Theory Ser. B 47 (1989), no. 2, 125--145. MR1047781 (91m:60038)
  7. Barbour, A. D.; Holst, Lars; Janson, Svante. Poisson approximation.Oxford Studies in Probability, 2. Oxford Science Publications.The Clarendon Press, Oxford University Press, New York, 1992. x+277 pp. ISBN: 0-19-852235-5 MR1163825 (93g:60043)
  8. Brown, Timothy C.; Xia, Aihua. Stein's method and birth-death processes. Ann. Probab. 29 (2001), no. 3, 1373--1403. MR1872746 (2002k:60039)
  9. Cekanavicius, V. Asymptotic expansions in the exponent: a compound Poisson approach. Adv. in Appl. Probab. 29 (1997), no. 2, 374--387. MR1450935 (98d:60042)
  10. Cekanavicius, V. Poisson approximations for sequences of random variables. Statist. Probab. Lett. 39 (1998), no. 2, 101--107. MR1652516 (99i:60046)
  11. Chyakanavichyus, V.; Vauitkus, P. Centered Poisson approximation by the Stein method.(Russian) Liet. Mat. Rink. 41 (2001), no. 4, 409--423; translation in Lithuanian Math. J. 41 (2001), no. 4, 319--329 MR1903485 (2003e:62031)
  12. Chen, Louis H. Y.; Shao, Qi-Man. Normal approximation under local dependence. Ann. Probab. 32 (2004), no. 3A, 1985--2028. MR2073183 (2005f:60054)
  13. Daley, D. J.; Vere-Jones, D. An introduction to the theory of point processes.Springer Series in Statistics. Springer-Verlag, New York, 1988. xxii+702 pp. ISBN: 0-387-96666-8 MR0950166 (90e:60060)
  14. Dembo, Amir; Karlin, Samuel. Poisson approximations for $r$-scan processes. Ann. Appl. Probab. 2 (1992), no. 2, 329--357. MR1161058 (94b:60021)
  15. Dembo, Amir; Rinott, Yosef. Some examples of normal approximations by Stein's method. Random discrete structures (Minneapolis, MN, 1993), 25--44, IMA Vol. Math. Appl., 76, Springer, New York, 1996. MR1395606 (97f:60051)
  16. Ehm, Werner. Binomial approximation to the Poisson binomial distribution. Statist. Probab. Lett. 11 (1991), no. 1, 7--16. MR1093412 (92b:60024)
  17. Gnedenko, B. V. On a local limit theorem of the theory of probability.(Russian) Uspehi Matem. Nauk (N. S.) 3, (1948). no. 3(25), 187--194. MR0026275 (10,132c)
  18. Götze, F.; Hipp, C. Asymptotic expansions for potential functions of i.i.d. random fields. Probab. Theory Related Fields 82 (1989), no. 3, 349--370. MR1001518 (90k:60042)
  19. Götze, F.; Hipp, C. Local limit theorems for sums of finite range potentials of a Gibbsian random field. Ann. Probab. 18 (1990), no. 2, 810--828. MR1055434 (91j:60041)
  20. Heinrich, Lothar. Asymptotic expansions in the central limit theorem for a special class of $m$-dependent random fields. I. Math. Nachr. 134 (1987), 83--106. MR0918670 (89e:60045)
  21. Heinrich, Lothar. Asymptotic expansions in the central limit theorem for a special class of $m$-dependent random fields. II. Lattice case. Math. Nachr. 145, (1990), 309--327.
  22. Kallenberg, Olav. Random measures.Fourth edition.Akademie-Verlag, Berlin; Academic Press, Inc., London, 1986. 187 pp. ISBN: 0-12-394960-2 MR0854102 (87k:60137)
  23. Le Cam, Lucien. On the distribution of sums of independent random variables. 1965 Proc. Internat. Res. Sem., Statist. Lab., Univ. California, Berkeley, Calif. pp. 179--202 Springer-Verlag, New York MR0199871 (33 #8011)
  24. bibitem [Mat{\'e}rn(1960)] B. Mat{\'e}rn (1960). \newblock Spatial variation: {S}tochastic models and their application to some problems in forest surveys and other sampling investigations. \newblock \emph{Meddelanden Fran Statens Skogsforskningsinstitut}, Band~49, Nr.~5. Stockholm.
  25. Reinert, Gesine. Couplings for normal approximations with Stein's method. Microsurveys in discrete probability (Princeton, NJ, 1997), 193--207, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 41, Amer. Math. Soc., Providence, RI, 1998. MR1630415 (99h:60043)
  26. Rinott, Yosef; Rotar, Vladimir. A multivariate CLT for local dependence with $n\sp {-1/2}\log n$ rate and applications to multivariate graph related statistics. J. Multivariate Anal. 56 (1996), no. 2, 333--350. MR1379533 (97a:60035)
  27. Röllin, Adrian. Approximation of sums of conditionally independent variables by the translated Poisson distribution. Bernoulli 11 (2005), no. 6, 1115--1128. MR2189083 (2006h:62019)
  28. Roos, Bero. Kerstan's method for compound Poisson approximation. Ann. Probab. 31 (2003), no. 4, 1754--1771. MR2016599 (2004m:60047)
  29. Sunklodas, \u I. Approximation of distributions of sums of weakly dependent random variables by the normal distribution.(Russian) Probability theory, 6 (Russian), 140--199, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1991. MR1157208 (93b:60050)
  30. Stein, Charles. A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, pp. 583--602. Univ. California Press, Berkeley, Calif., 1972. MR0402873 (53 #6687)
  31. Stein, Charles. Approximate computation of expectations.Institute of Mathematical Statistics Lecture Notes---Monograph Series, 7. Institute of Mathematical Statistics, Hayward, CA, 1986. iv+164 pp. ISBN: 0-940600-08-0 MR0882007 (88j:60055)
  32. Tihomirov, A. N. Convergence rate in the central limit theorem for weakly dependent random variables.(Russian) Teor. Veroyatnost. i Primenen. 25 (1980), no. 4, 800--818. MR0595140 (82h:60050)


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