Maximum and minimum of modified gambler's ruin problem

Abstract

We obtain maximum and minimum of modified gambler's ruin problem by studying discrete random walk with absorbing barriers on the boundary. The modification is that our process can move one step forward or backward (standard gambler's ruin problem), but we have also the possibilty to stay where we are for a time unit or there can be absorption in the current state (game is terminated without reaching an absorbing barrier).Comment: 13 page