Geodesic
On some inequalities in boundary crossing problems for random walks
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 661-671

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We obtain new upper and lower bounds for the probability that random walk with negative drift leaves the strip through the upper boundary. It is assumed that distributions of the walk increments do not have an exponential moment. The accuracy of known inequalities for the distribution of trajectory supremum is analyzed.
Keywords: random walk, two-sided boundary crossing problem, ruin probability, trajectory supremum. 
@article{SEMR_2020_17_a43,
     author = {V. I. Lotov},
     title = {On some inequalities in boundary crossing problems for random walks},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {661--671},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a43/}
}
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V. I. Lotov. On some inequalities in boundary crossing problems for random walks. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 661-671. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a43/