Geodesic
Large-Deviation Probabilities for Maxima of Sums of Independent Random Variables with Negative Mean and Subexponential Distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 2, pp. 387-397 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the sums $S_n=\xi_1+\dots+\xi_n$ of independent identically distributed random variables with negative mean value. In the case of subexponential distribution of the summands, the asymptotic behavior is found for the probability of the event that the maximum of sums $\max(S_1,\ldots,S_n)$ exceeds high level $x$. The asymptotics obtained describe this tail probability uniformly with respect to all values of $n$.
Keywords: maxima of sums of random variables, homogeneous Markov chain, large deviation probabilities, subexponential distribution, integrated tail distribution. 
@article{TVP_2001_46_2_a14,
     author = {D. A. Korshunov},
     title = {Large-Deviation {Probabilities} for {Maxima} of {Sums} of {Independent} {Random} {Variables} with {Negative} {Mean} and {Subexponential} {Distribution}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {387--397},
     year = {2001},
     volume = {46},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_2_a14/}
}
TY  - JOUR
AU  - D. A. Korshunov
TI  - Large-Deviation Probabilities for Maxima of Sums of Independent Random Variables with Negative Mean and Subexponential Distribution
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2001
SP  - 387
EP  - 397
VL  - 46
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TVP_2001_46_2_a14/
LA  - ru
ID  - TVP_2001_46_2_a14
ER  - 
%0 Journal Article
%A D. A. Korshunov
%T Large-Deviation Probabilities for Maxima of Sums of Independent Random Variables with Negative Mean and Subexponential Distribution
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2001
%P 387-397
%V 46
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_2001_46_2_a14/
%G ru
%F TVP_2001_46_2_a14
D. A. Korshunov. Large-Deviation Probabilities for Maxima of Sums of Independent Random Variables with Negative Mean and Subexponential Distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 2, pp. 387-397. http://geodesic.mathdoc.fr/item/TVP_2001_46_2_a14/