Geodesic
On one property of symmetrized distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 1, pp. 68-71 Cet article a éte moissonné depuis la source Math-Net.Ru

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The present paper studies the connection between the local limit theorem for lattice random variables and the corresponding symmetrized random variables. An example is constructed to show that the local limit theorem holds for some sequence of symmetrized random variables, but fails to hold for the original random variables.
Keywords: local limit theorem for lattice random variables, local limit theorem for symmetrized random variables. 
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N. G. Gamkrelidze. On one property of symmetrized distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 1, pp. 68-71. http://geodesic.mathdoc.fr/item/TVP_2017_62_1_a4/

[1] P. Lévy, “Sur les intégrales dont les éléments sont des variables aléatoires indépendantes”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2), III:3-4 (1934), 337–366 | MR | Zbl

[2] B. V. Gnedenko, “O kharakteristicheskikh funktsiyakh”, Byulleten MGU. Sekts. A. Matem. i mekh., 1:5 (1937), 17–18

[3] B. V. Gnedenko, “O lokalnoi teoreme dlya predelnykh ustoichivykh raspredelenii”, Ukr. matem. zhurn., 1:4 (1949), 3–15 | MR | Zbl

[4] N. G. Gamkrelidze, “On a lower bound for the rate of convergence in the local limit theorem”, Select. Transl. Math. Statist. and Probability, 11, Amer. Math. Soc., Providence, RI, 1973, 117–120 | MR | Zbl | Zbl

[5] N. Gamkrelidze, “On one inequality for characteristic functions”, Prokhorov and contemporary probability theory, Springer Proc. Math. Stat., 33, Springer, Heidelberg, 2013, 275–280 | DOI | MR | Zbl

[6] L. Chaumont, M. Yor, Exercises in probability. A guided tour from measure theory to random processes, via conditioning, Camb. Ser. Stat. Probab. Math., 13, Cambridge Univ. Press, Cambridge, 2003, xvi+236 pp. | DOI | MR | Zbl

[7] Yu. V. Prokhorov, “Predelnye teoremy dlya summ nezavisimykh sluchainykh velichin”, dis. ... kand. fiz.-matem. nauk, 1952, Izbrannye trudy, Torus Press, M., 2012, 57–92

[8] G. Székély, Paradoxes in probability theory and mathematical statistics, Math. Appl. (East Eur. Ser.), 15, D. Reidel Publ. Co., Dordrecht; Akademiai Kiado, Budapest, 1986, xii+250 pp. | MR | Zbl | Zbl

[9] J. M. Stoyanov, Counterexamples in probability, Wiley Ser. Probab. Math. Stat., John Wiley Sons, Ltd., Chichester, 1987, xxiv+313 pp. | MR | Zbl | Zbl

[10] W. Feller, An introduction to probability theory and its applications, v. 1, 2, John Wiley Sons, Inc., New York–London–Sydney, 1968, 1971, xviii+509 pp., xxiv+669 pp. | MR | MR | Zbl | Zbl

[11] A. Khintchine, “Contribution à l'arithmétique des lois de distribution”, Byulleten MGU. Sekts. A. Matem. i mekh., 1:1 (1937), 6–17 | Zbl