Abstract
For a large variety of new products, the Bass Model (BM) describes the empirical cumulative-adoptions curve extremely well. The BM postulates that the trajectory of cumulative adoptions of a new product follows a deterministic function whose instantaneous growth rate depends on two parameters, one of which captures an individual's intrinsic tendency to purchase, independent of the number of previous adopters, and the other captures a positive force of influence on an individual by previous adopters. In this paper, we formulate a stochastic version of the BM, which we call the Stochastic Bass Model (SBM), where the trajectory of cumulative number of adoptions is governed by a pure birth process. We show that with an appropriately-chosen set of birth rates, the fractions of individuals who have adopted the product by time