Geodesic
On the asymptotics of the distribution of excess
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 292-299.

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

We find asymptotic expansion in the powers of $e^{-b}$ for the distribution of excess over boundary $b\to\infty$ under one-sided Cramér condition on the distribution of random walk summands. As a corollary, we obtain asymptotic expansion for the renewal function.
Keywords: random walk, excess over boundary, renewal function, asymptotic expansions. 
@article{SEMR_2015_12_a33,
     author = {V. I. Lotov},
     title = {On the asymptotics of the distribution of excess},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {292--299},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a33/}
}
TY  - JOUR
AU  - V. I. Lotov
TI  - On the asymptotics of the distribution of excess
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2015
SP  - 292
EP  - 299
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2015_12_a33/
LA  - ru
ID  - SEMR_2015_12_a33
ER  - 
%0 Journal Article
%A V. I. Lotov
%T On the asymptotics of the distribution of excess
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2015
%P 292-299
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2015_12_a33/
%G ru
%F SEMR_2015_12_a33
V. I. Lotov. On the asymptotics of the distribution of excess. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 292-299. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a33/

[1] V. I. Lotov, “Asymptotic Expansions in a Sequential Likelihood Ratio Test”, Theory Probab. Appl., 32 (1988), 57–67 | DOI | MR

[2] A. A. Borovkov, Probability Theory, Springer, London, 2013 | MR | Zbl

[3] J. H. B. Kemperman, “A Wiener–Hopf type method for a general random walk with a two-sided boundary”, Annals of Mathematical Statistics, 34 (1963), 1168–1193 | DOI | MR | Zbl

[4] V. I. Lotov, “On an approach to problems with two boundaries”, Statistics and Control of Random Processes, Nauka, M., 1989, 117–121 (in Russian) | MR

[5] A. A. Borovkov, Stochastic processes in queueing theory, Springer, New York, 1976 | MR | Zbl

[6] V. I. Lotov, “Asymptotic behavior of the distribution of the supremum of successive sums”, Math. Notes, 38 (1985), 876–882 | DOI | MR | Zbl

[7] V. I. Lotov, “On some boundary crossing problems for Gaussian random walks”, Annals of Probability, 24 (1996), 2154–2171 | DOI | MR | Zbl