Doney, R AMaller, RossSavov, Mladen2015-12-080304-4149http://hdl.handle.net/1885/32812Renewal-like results and stability theorems relating to the large-time behaviour of a random walk Sn reflected in its maximum, Rn = max0 ≤ j ≤ n Sj - Sn, are proved. Mainly, we consider the behaviour of the exit time, τ (r), where τ (r) = min {n ≥Keywords: Exit time; Overshoot; Passage times; Random walks; Reflected process; Renewal theorems; Stability theorems; Human computer interaction Overshoot; Passage times; Reflected process; Renewal theorems200810.1016/j.spa.2008.06.0092016-02-24