Geodesic
Supremum asymptotics for random walk with switching
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 999-1020

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

We consider random walk $X_n, n\geq 0$ with one level of switching $a\leq 0.$ Some theorems on the asymptotics of the supremum distribution $\mathbf{P}\left(\sup\limits_{n} X_n>x\right)$ as $x\to\infty,$ $a\to -\infty$ were obtained in Cramer case.
Keywords: random walk with switching, supremum asymptotics. 
@article{SEMR_2014_11_a38,
     author = {D. K. Kim},
     title = {Supremum asymptotics for random walk with switching},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {999--1020},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a38/}
}
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D. K. Kim. Supremum asymptotics for random walk with switching. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 999-1020. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a38/