### ON ASYMPTOTIC BEHAVIOR OF CONDITIONAL PROBABILITY OF CROSSING THE NONLINEAR BOUNDARY BY A PERTURBED RANDOM WALK

**S. Aliyev, F. Rahimov, M. Navidi**

*Theory of Stochastic Processes*

*Vol.17 (33), no.1, 2011, pp.5-11*

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 $\alpha \in (1,2]$.