A note on the distribution of response times for a random walk with Gaussian increments

Abstract

In this note, response time distribution predictions for the two-absorbing-barrier Gaussian-increments random walk in discrete time are derived. This derivation, which neglects the excess over the absorbing barriers on termination, involves an implicit limiting operation on the interval between increments to the walk, thereby approximating the discrete time random walk with a continuous time Wiener diffusion process. Two simple procedures for correcting for the excess over the absorbing barriers are considered, which increase the barriers by an estimate of the expected value of the excess. These corrections substantially improve the accuracy of the predictions, as shown by the fit between theoretical and simulated distributions. One implication of this result is that it is unlikely to be possible to distinguish between discrete and continuous sampling models on the basis of goodness of fit indices alone.