Large deviation probabilities for some classes of distributions, satisfying the Cramer condition
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 161-185 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the note limit theorems on large deviations of sum $X_1+\cdots+X_n$ of i.i.d. random variables under the assumption $\mathbf E X^2_1\,e^{\la X_1}<\infty $ for some $\lambda>0$ are studied.
@article{ZNSL_2003_298_a10,
     author = {L. V. Rozovskii},
     title = {Large deviation probabilities for some classes of distributions, satisfying the {Cramer} condition},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {161--185},
     year = {2003},
     volume = {298},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a10/}
}
TY  - JOUR
AU  - L. V. Rozovskii
TI  - Large deviation probabilities for some classes of distributions, satisfying the Cramer condition
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 161
EP  - 185
VL  - 298
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a10/
LA  - ru
ID  - ZNSL_2003_298_a10
ER  - 
%0 Journal Article
%A L. V. Rozovskii
%T Large deviation probabilities for some classes of distributions, satisfying the Cramer condition
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 161-185
%V 298
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a10/
%G ru
%F ZNSL_2003_298_a10
L. V. Rozovskii. Large deviation probabilities for some classes of distributions, satisfying the Cramer condition. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 161-185. http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a10/

[1] G. Kramer, “Ob odnoi novoi teoreme teorii veroyatnostei”, Uspekhi matem. nauk, 1944, no. X, 166–178

[2] V. V. Petrov, “O veroyatnostyakh bolshikh uklonenii summ nezavisimykh sluchainykh velichin”, Teoriya veroyatn. i ee primen., 10:2 (1965), 310–322 | MR | Zbl

[3] R. R. Bahadur, Rao R. Ranga, “On deviations of the sample mean”, Ann. Math. Stat., 31:4 (1960), 1015–1027 | DOI | MR | Zbl

[4] A. A. Borovkov, B. A. Rogozin, “O tsentralnoi predelnoi teoreme v mnogomernom sluchae”, Teoriya veroyatn. i ee primen., 10:1 (1965), 61–69 | MR | Zbl

[5] T. Höglund, “A unified formulation of the central limit theorem for small and large deviations from the mean”, Z. Wahrscheinlichkeitstheor. verw. Geb., 49 (1979), 105–117 | DOI | MR | Zbl

[6] A. V. Nagaev, “The Cramer large deviations when the extreme conjugate distribution is heavy-tailed”, Teoriya veroyatn. i ee primen., 43:3 (1998), 456–475 | MR | Zbl

[7] B. von Bahr, “Multi-dimensional integral limit theorems for large deviations”, Ark. Mat., 7 (1967), 89–99 | DOI | MR | Zbl

[8] L. V. Osipov, “On large deviations for sums of random vectors in $R_k$”, J. Mult. Anal., 11:2 (1981), 115–126 | DOI | MR | Zbl

[9] L. V. Kim, A. V. Nagaev, “O nesimmetrichnoi probleme bolshikh uklonenii”, Teoriya veroyatn. i ee primen., 22:2 (1977), 335–346 | MR

[10] L. V. Rozovskii, “Veroyatnosti bolshikh uklonenii na vsei osi”, Teoriya veroyatn. i ee primen., 38:1 (1993), 79–109 | MR | Zbl

[11] L. V. Rozovskii, “Veroyatnosti bolshikh uklonenii summ nezavisimykh sluchainykh velichin s obschei funktsiei raspredeleniya iz oblasti prityazheniya normalnogo zakona”, Teoriya veroyatn. i ee primen., 34:4 (1989), 686–705 | MR

[12] L. V. Rozovskii, “O predelnykh teoremakh dlya bolshikh uklonenii v uzkikh zonakh”, Teoriya veroyatn. i ee primen., 26:4 (1981), 847–857 | MR | Zbl

[13] L. V. Rozovsky, “Asymptotic Expansions for Probabilities of Large Deviations”, Probab. Theor. Related Fields, 73:2 (1986), 299–318 | DOI | MR | Zbl

[14] V. V. Petrov, Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972 | MR

[15] L. V. Rozovsky, “Large deviation probabilities for sums of independent unlattice random variables under unilateral Cramer condition”, 22nd European Meeting of Statisticians, 7th Vilnius Conf. on Probab. Theory and Math. Stat., Abstracts, TEV, Vilnius, 1998, 394

[16] L. V. Rozovskii, “O tochnosti normalnogo priblizheniya”, Zap. nauchn. semin. LOMI, 177, 1989, 129–137 | MR | Zbl

[17] L. V. Rozovskii, “O neravenstve Duba dlya kharakteristicheskikh funktsii”, Teoriya veroyatn. i ee primen., 44:3 (1999), 650–652 | MR | Zbl