On the calculation of mean first passage times for simple random walks

The equivalence of two recently proposed methods for calculating mean first passage times in unit-step, one-dimensional random walks is established. An intermediate result of the demonstration is a new analytic expression for the mean accumulated residence time in any particular state. This expression is used to obtain some simple approximate results concerning (i) extreme fluctuations in unimodal systems and (ii) transitions between steady states in bimodal systems.