On the relations between random walk models for two-choice response times

We state a condition on the moment-generating functions of the random walk model derived by Link and Heath (1975), which is necessary and sufficient to yield the sequential probability ratio test of Wald (1947) and the reaction-time model proposed by Stone (1960). A restricted form of this condition can also be obtained by imposing the types of symmetries on the moment-generating functions considered by Link and Health (1975) and Thomas (1975). The various conditions are contrasted and their implications for empirical investigation are discussed.