S. Aliyev, F. Rahimov, M. Navidi, “On asymptotic behaviour of conditional probability of crossing the nonlinear boundary by a perturbed random walk”, Theory Stoch. Process., 2011, Volume 17(33), Issue 1,Pages <nobr>5

On asymptotic behaviour of conditional probability of crossing the nonlinear boundary by a perturbed random walk

S. Aliyev^a, F. Rahimov^b, M. Navidi

^a Institute of Mathematics and Mechanics of the NAS of Azerbaijan
^b Department of Probability Theory and Mathematical Statistics of the State University of Baku

Abstract: 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.

MSC: 60G50

Language: English