On asymptotic behavior of local probabilities of crossing the nonlinear boundaries by a perturbed random walk

• Asymptotic behavior of cross nonlinear boundary using random walk has studied.
• We obtained the distribution of overshoots for nonlinear boundary.
• We proved that the density of first passage time tends to the normal.

In this paper, theorems on the asymptotic behavior of local probabilities of crossing nonlinear boundary by a perturbed random walk were proved.