Geodesic
On the necessary conditions of Poisson convergence
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 813-816 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper proves a theorem on necessary conditions for the Poisson convergence of sums of martingale differences. The theorem conditions generalize the classic conditions for the convergence of sums of independent summands.
Mots-clés : martingale, Poisson law
Keywords: weak convergenceю. 
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A. G. Sholomitskii. On the necessary conditions of Poisson convergence. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 813-816. http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a13/

[1] Brown B., Eagleson G. K., “Martingale convergence to infinitely divisible laws with finite variance”, Trans. Amer. Math. Soc., 162 (1971), 449–453 | DOI | MR

[2] Brown B., “Martingale central limit theorems”, Ann. Math. Statist., 42 (1971), 59–66 | DOI | MR | Zbl

[3] Zhakod Zh., Shiryaev A. N., Predelnye teoremy dlya sluchainykh protsessov, v. 1, 2, Nauka, M., 1994, 544 pp. ; 368 с. | MR

[4] Liptser R. Sh., Shiryaev A. N., “Funktsionalnaya tsentralnaya predelnaya teorema dlya semimartingalov”, Teoriya veroyatn. i ee primen., 25:4 (1980), 683–703 | MR | Zbl

[5] Liptser R. Sh., Shiryaev A. N., Teoriya martingalov, Nauka, M., 1986, 512 pp. | MR | Zbl

[6] Sholomitskii A. G., “O neobkhodimykh usloviyakh normalnoi skhodimosti dlya martingalov”, Teoriya veroyatn. i ee primen., 43:3 (1998), 490–508 | MR