Journal of Applied Probability

A stochastic two-stage innovation diffusion model on a lattice

Cristian F. Coletti, Karina B. E. de Oliveira, and Pablo M. Rodriguez

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We propose a stochastic model describing a process of awareness, evaluation, and decision making by agents on the d-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0, 1, 2. In this model 0 stands for ignorants, 1 for aware, and 2 for adopters. Aware and adopters inform its nearest ignorant neighbors about a new product innovation at rate λ. At rate α an agent in aware state becomes an adopter due to the influence of adopters' neighbors. Finally, aware and adopters forget the information about the new product, thus becoming ignorant, at rate 1. Our purpose is to analyze the influence of the parameters on the qualitative behavior of the process. We obtain sufficient conditions under which the innovation diffusion (and adoption) either becomes extinct or propagates through the population with positive probability.

Article information

J. Appl. Probab., Volume 53, Number 4 (2016), 1019-1030.

First available in Project Euclid: 7 December 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60K10: Applications (reliability, demand theory, etc.) 60J28: Applications of continuous-time Markov processes on discrete state spaces

Interacting particle system innovation diffusion stochastic model Bass model contact process oriented percolation


Coletti, Cristian F.; de Oliveira, Karina B. E.; Rodriguez, Pablo M. A stochastic two-stage innovation diffusion model on a lattice. J. Appl. Probab. 53 (2016), no. 4, 1019--1030.

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