Geodesic
Small deviation probabilities for sums of independent positive random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 151-167
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the note we give estimates of small deviation probabilities of a sum $\sum_{j\ge 1} \lambda_j X_j$, where $\{\lambda_j\}$ are nonnegative numbers and $\{X_j\}$ are i.i.d. positive random variables, satisfying mild assumptions at zero and infinity. 
@article{ZNSL_2007_341_a10,
     author = {L. V. Rozovskii},
     title = {Small deviation probabilities for sums of independent positive random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {151--167},
     year = {2007},
     volume = {341},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a10/}
}
TY  - JOUR
AU  - L. V. Rozovskii
TI  - Small deviation probabilities for sums of independent positive random variables
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2007
SP  - 151
EP  - 167
VL  - 341
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a10/
LA  - ru
ID  - ZNSL_2007_341_a10
ER  - 
%0 Journal Article
%A L. V. Rozovskii
%T Small deviation probabilities for sums of independent positive random variables
%J Zapiski Nauchnykh Seminarov POMI
%D 2007
%P 151-167
%V 341
%U http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a10/
%G ru
%F ZNSL_2007_341_a10
L. V. Rozovskii. Small deviation probabilities for sums of independent positive random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 151-167. http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a10/

[1] Rozovskii L. V., “O veroyatnostyakh malykh uklonenii nekotorykh sluchainykh summ”, Obozrenie prikladnoi i promysh. matematiki, 12:4 (2005), 865–866 | MR

[2] Lifshits M. A., “On the lower tail probabilities of some random series”, Ann. Probab., 25 (1997), 424–442 | DOI | MR | Zbl

[3] R. Davis, S. Resnick, “Extremes of moving averages of random variables with finite endpoint”, Ann. Probab., 19 (1991), 312–328 | DOI | MR | Zbl

[4] Rozovskii L. V., “O veroyatnostyakh malykh uklonenii polozhitelnykh sluchainykh velichin”, Zapiski nauchn.semin. POMI, 320, 2004, 150–159 | Zbl

[5] Rozovskii L. V., “O nizhnei granitse veroyatnostei bolshikh uklonenii dlya vyborochnogo srednego pri vypolnenii usloviya Kramera”, Zapiski nauchn.semin. POMI, 278, 2001, 208–224 | MR | Zbl

[6] Rozovskii L. V., “Veroyatnosti malykh uklonenii dlya odnogo klassa raspredelenii so stepennym ubyvaniem v nule”, Zapiski nauchn.semin. POMI, 328, 2005, 182–190 | MR

[7] Aurzada F., “On the lower tail probabilities of some random sequences in $l_p$”, Unpablished manuscript, 2006 | MR | Zbl

[8] Borovkov A. A., Ruzankin P. S., “On small deviations of series of weighted i.i.d. random variables”, Limit theorems in Probability Theory and Their Applications, IV International Conf., Absracts (Novosibirsk, 21–25 August), 2006, 14

[9] N. C. Jain, W. E. Pruitt, “Lower tail probability estimates for subordinators and nondecreasing random walks”, Ann. Probab., 15:1 (1987), 76–101 | DOI | MR

[10] V. V. Petrov, Predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Nauka, M., 1987, 320 pp. | MR