Geodesic
Asymptotic formulas for probabilities of
Teoriâ slučajnyh processov, Tome 14 (2008) no. 1, pp. 100-116.

Voir la notice de l'article provenant de la source Math-Net.Ru

Asymptotic formulas for large-deviation probabilities of a ladder height in a random walk generated by a sequence of sums of i.i.d. random variables are deduced. Two cases are considered: 
@article{THSP_2008_14_1_a11,
     author = {Sergey V. Nagaev},
     title = {Asymptotic formulas for probabilities of},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {100--116},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a11/}
}
TY  - JOUR
AU  - Sergey V. Nagaev
TI  - Asymptotic formulas for probabilities of
JO  - Teoriâ slučajnyh processov
PY  - 2008
SP  - 100
EP  - 116
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a11/
LA  - en
ID  - THSP_2008_14_1_a11
ER  - 
%0 Journal Article
%A Sergey V. Nagaev
%T Asymptotic formulas for probabilities of
%J Teoriâ slučajnyh processov
%D 2008
%P 100-116
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a11/
%G en
%F THSP_2008_14_1_a11
Sergey V. Nagaev. Asymptotic formulas for probabilities of. Teoriâ slučajnyh processov, Tome 14 (2008) no. 1, pp. 100-116. http://geodesic.mathdoc.fr/item/THSP_2008_14_1_a11/

[1] W. Feller, An Introduction to Probability Theory and Its Applications, v. II, Wiley, New York, 1967 | MR

[2] S. V. Nagaev, S. S. Khodzhabagjan, “On an estimate of the concentration function of sums of independent random variables”, Theory Probab. Appl., 41:3 (1996), 560–568 | MR

[3] P. Greenwood, I. Omey, J. L. Teugels, “Harmonic renewal measures”, Z.Warsch. Verw. Gebiete, 59 (1982), 391–409 | DOI | MR | Zbl

[4] P. Greenwood, I. Omey, J. L. Teugels, “Harmonic renewal measures and bivariate domains of attractions in fluctuation theory”, Z. Warsch. Verw. Gebiete, 61 (1982), 527–539 | DOI | MR | Zbl

[5] R. J. Grubel, “On harmonic renewal measures”, Probab. Theory Rel. Fields, 71 (1986), 393–403 | DOI | MR

[6] R. J. Grubel, “Harmonic renewal sequences and the first positive sum”, J. London Math. Soc., 38:2 (1988), 179–192 | DOI | MR | Zbl

[7] A. J. Stam, “Some theorems on harmonic renewal measures”, Stochastic processes and their Appl., 39 (1991), 277–285 | DOI | MR | Zbl

[8] L. de Haan, “An Abel–Tauber theorem for Laplace transforms”, J. London Math. Soc., 13:3 (1976), 537–542 | DOI | MR | Zbl

[9] R. A. Doney, “Moments of ladder heights in random walks”, J. Appl. Probab., 17 (1980), 248–252 | DOI | MR | Zbl

[10] B. A. Rogosin, “On the distribution of the first jump”, Theory Probab. Appl., 9 (1964), 450–465 | DOI | MR

[11] N. Veraverbeke, “Asymptotic behaviour of Wiener-Hopf factors of a random walk”, Stochastic processes and their Appl., 5 (1977), 27–37 | DOI | MR | Zbl

[12] P. Embrechts, C. M. Goldie, N. Vereverbeke, “Subexponentiality and infinite divisibility”, Z. Warsch. Verw. Gebiete, 49 (1979), 335–347 | DOI | MR | Zbl

[13] R. Grubel, “Tail behaviour of ladder–height distibulions in random walks”, J. Appl. Probab., 22 (1985), 705–709 | DOI | MR | Zbl

[14] S. V. Nagaev, Exact expressions for moments of ladder heigsts, Preprint 2007/192., IM SO RAN, Novosibirsk, 2007 (In Russian) | MR

[15] S. V. Nagaev, “The formula for the Laplace transform of the projection of a distribution on the positive semiaxis and some its applications”, Dokl. Math., 416:5 (2007) | MR

[16] B. Rosen, “On the asymptotic distribution of sums of independent indentically distributed random variables”, Ark.Mat., 4:4 (1962), 323–332 | DOI | MR | Zbl

[17] I. S. Gradshtein, I. M. Ryzhik, Tables of integrals, sums, series and products, Fiz. Mat. Giz., Moscow, 1963 | MR