Some exact results for random walk models with applications

This article presents a random walk model that can be analyzed without recourse to Wald's (1947) approximation, which neglects the excess over the absorbing barriers. Hence, the model yields exact predictions for the absorption probabilities and all mean conditional absorption times. We derive these predictions in some detail and fit them to the extensive data of an identification experiment published by Green et al. (1983). The fit of the model seems satisfactory. The relationship of the model to existing classes of random walk models (SPRT and SSR; see Luce, 1986) is discussed; for certain combinations of its parameters, the model belongs either to the SPRT or to the SSR class, or to both. We stress the theoretical significance of the knowledge of exact results for the evaluation of Wald's approximation and general properties of the several models proposed derived from this approximation.