@article{ZNSL_2017_466_a7,
author = {F. G\"otze and A. Yu. Zaitsev},
title = {Rare events and {Poisson} point processes},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {109--119},
year = {2017},
volume = {466},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a7/}
}
F. Götze; A. Yu. Zaitsev. Rare events and Poisson point processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 109-119. http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a7/
[1] T. V. Arak, “O skorosti skhodimosti v ravnomernoi predelnoi teoreme Kolmogorova. I”, Teoriya veroyatn. i ee primen., 26:2 (1981), 225–245 | MR | Zbl
[2] T. V. Arak, A. Yu. Zaitsev, Ravnomernye predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Tr. MIAN SSSR, 174, 1986, 214 pp. | MR | Zbl
[3] A. D. Barbour, O. Chryssaphinou, “Compound Poisson approximation: a user's guide”, Ann. Appl. Probab., 33 (2001), 727–750 | DOI | MR | Zbl
[4] A. D. Barbour, P. Hall, “On the rate of Poisson convergence”, Math. Proc. Camb. Phil. Soc., 95 (1984), 473–480 | DOI | MR | Zbl
[5] I. Berkes, W. Philipp, “Approximation theorems for independent and weakly dependent random vectors”, Ann. Probab., 7 (1979), 29–54 | DOI | MR | Zbl
[6] R. M. Dudley, “Distances of probability measures and random variables”, Ann. Math. Statist., 39 (1968), 1563–1572 | DOI | MR | Zbl
[7] F. Götze, A. Yu. Zaitsev, “Approximation of convolutions by accompanying laws without centering”, Zap. nauchn. semin. POMI, 320, 2004, 44–53 | MR | Zbl
[8] I. A. Ibragimov, E. L. Presman, “O skorosti sblizheniya raspredelenii summ nezavisimykh sluchainykh velichin s soprovozhdayuschimi zakonami”, Teoriya veroyatn. i ee primen., 18:4 (1973), 753–766 | MR | Zbl
[9] M. Katz, “Note on the Berry–Esseen theorem”, Ann. Math. Statist., 34:4 (1963), 1107–1108 | DOI | MR | Zbl
[10] A. N. Kolmogorov, “O priblizhenii raspredelenii summ nezavisimykh slagaemykh neogranichenno delimymi raspredeleniyami”, Trudy Moskovsk. matem. ob-va, 12, 1963, 437–451 | MR | Zbl
[11] L. Le Cam, “An approximation theorem for Poisson binomial distribution”, Pacific J. Math., 10 (1960), 1181–1197 | DOI | MR | Zbl
[12] L. Le Cam, “On the distribution of sums of independent random variables”, Bernoulli, Bayes, Laplace, Anniversary volume, Springer, Berlin, 1965, 179–202
[13] L. Le Cam, Asymptotic Methods in Statistical Decision Theory, Springer, Berlin, 1986 | MR | Zbl
[14] V. V. Petrov, “Odna otsenka otkloneniya raspredeleniya summy nezavisimykh sluchainykh velichin ot normalnogo zakona”, Dokl. AN SSSR, 160:5 (1965), 1013–1015 | MR | Zbl
[15] Yu. V. Prokhorov, “Asimptoticheskoe povedenie binomialnogo raspredeleniya”, Uspekhi matem. nauk, 8:3 (1953), 135–142 | MR | Zbl
[16] A. Yu. Zaitsev, “O tochnosti approksimatsii raspredelenii summ nezavisimykh sluchainykh velichin, otlichnykh ot nulya s maloi veroyatnostyu, s pomoschyu soprovozhdayuschikh zakonov”, Teoriya veroyatn. i ee primen., 28:4 (1983), 625–636 | MR | Zbl
[17] A. Yu. Zaitsev, “O ravnomernoi approksimatsii funktsii raspredeleniya summ nezavisimykh sluchainykh velichin”, Teoriya veroyatn. i ee primen., 32:1 (1987), 45–52 | MR | Zbl
[18] A. Yu. Zaitsev, “Mnogomernyi variant vtoroi ravnomernoi predelnoi teoremy Kolmogorova”, Teoriya veroyatn. i ee primen., 34:1 (1989), 128–151 | MR | Zbl
[19] A. Yu. Zaitsev, “Approksimatsiya svertok veroyatnostnykh raspredelenii bezgranichno delimymi zakonami pri oslablennykh momentnykh ogranicheniyakh”, Zap. nauchn. semin. POMI, 194, 1992, 79–90 | MR
[20] A. Yu. Zaitsev, “Ob approksimatsii vyborki puassonovskim tochechnym protsessom”, Zap. nauchn. semin. POMI, 298, 2003, 111–125 | MR | Zbl