Hitting Time of a Half-Line by a Two-Dimensional Non-Symmetric Random Walk

Abstract

Abstract. We consider the probability that a two-dimensional random walk starting from the origin never returns to the half-line (−∞, 0] × {0} before time n. Let X = (X 1 , X 2 ) be the increment of the two-dimensional random walk. For an aperiodic random walk with moment conditions E[X 2 ] = 0 and, we obtain an asymptotic estimate (as n → ∞) of this probability by assuming the behavior of the characteristic function of X near zero.