A stochastic formulation of the Bass model of new-product diffusion
type: Item
instance of: scholarly article
title: A stochastic formulation of the Bass model of new-product diffusion
zbMATH Open document ID: 1062.90518
DOI: 10.1080/10241230215285
author: Shun-Chen Niu
published in: Mathematical Problems in Engineering
publication date: 2004-08-23T00:00:00Z
review text: Summary: For 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. We formulate a stochastic version of the BM, which we call the stochastic Bass model (SBM), where the trajectory of the 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.
Mathematics Subject Classification ID: 90B60
Mathematics Subject Classification ID: 60J85
zbMATH DE Number: 2094353
zbMATH Keywords: pure birth processes
zbMATH Keywords: diffusion models
zbMATH Keywords: new-product adoptions
zbMATH Keywords: epidemics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1080/10241230215285
OpenAlex ID: W3124807475
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description: scientific article; zbMATH DE number 2094353