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On asymptotic behaviour of conditional probability of crossing the nonlinear boundary by a perturbed random walk. (English) Zbl 1249.60084
Summary: We prove a theorem on the limit behaviour 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 $$\alpha\in (1,2]$$.

##### MSC:
 60G50 Sums of independent random variables; random walks
##### Keywords:
perturbed random walk; stable law; domain of attraction