Geodesic
On asymptotic behaviour of conditional probability of crossing the nonlinear boundary by a perturbed random walk
Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 5-11

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We prove a theorem on the limit behavior of the conditional probability of crossing the nonlinear boundary by a perturbed random walk with a distribution which belongs to the domain of attraction of the stable law with index $\alpha \in \left( 1,2\right].$
Keywords: Perturbed random walk, first passage time, conditional probability of crossing the boundary, overshoot of a random walk. 
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     author = {S. Aliyev and F. Rahimov and M. Navidi},
     title = {On asymptotic behaviour of conditional probability of crossing the nonlinear boundary by a perturbed random walk},
     journal = {Teori\^a slu\v{c}ajnyh processov},
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     publisher = {mathdoc},
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     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a0/}
}
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S. Aliyev; F. Rahimov; M. Navidi. On asymptotic behaviour of conditional probability of crossing the nonlinear boundary by a perturbed random walk. Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 5-11. http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a0/