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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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.

Article information

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

Dates
First available in Project Euclid: 7 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1481132833

Mathematical Reviews number (MathSciNet)
MR3581238

Zentralblatt MATH identifier
1356.60164

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.jap/1481132833


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