a stochastic formulation of the bass model of new-product diffusion

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ID: 166206
2002
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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 t in a family of SBMs indexed by the size of the target population converge in probability to the deterministic fraction in a corresponding BM, when the population size approaches infinity. The formulation therefore supports and expands the BM by allowing stochastic trajectories.

Reference Key
shun-chen2002mathematicala Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Niu Shun-Chen
Journal journal of power sources
Year 2002
DOI
DOI not found
URL
http://www.hindawi.net/access/get.aspx?journal=mpe&volume=8&pii=S1024123X02001977
Keywords
civil engineering (general)mathematics

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