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December 2016 A stochastic two-stage innovation diffusion model on a lattice
Cristian F. Coletti, Karina B. E. de Oliveira, Pablo M. Rodriguez
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J. Appl. Probab. 53(4): 1019-1030 (December 2016).

Abstract

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.

Citation

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Cristian F. Coletti. Karina B. E. de Oliveira. Pablo M. Rodriguez. "A stochastic two-stage innovation diffusion model on a lattice." J. Appl. Probab. 53 (4) 1019 - 1030, December 2016.

Information

Published: December 2016
First available in Project Euclid: 7 December 2016

zbMATH: 1356.60164
MathSciNet: MR3581238

Subjects:
Primary: 60K35
Secondary: 60J28, 60K10

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 4 • December 2016
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