Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-18T19:40:55.820Z Has data issue: false hasContentIssue false
  • English
  • Français

An improved stochastic model allowing interaction among individuals

Published online by Cambridge University Press:  14 July 2016

P. B. Cerrito
P. B. Cerrito*
Affiliation:
University of South Florida
*
∗ Postal address: Department of Mathematics, University of South Florida, Tampa, FL 33620, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

The purpose of this paper is to explore the properties of a new model which can describe the interaction among individuals. Various other models have been proposed, but all assume that each individual acts independently of all others. Our model permits the assumption that individuals can be influenced and dominated by other individuals. We also demonstrate how this model can describe the interaction of various species in an ecosystem. This model will lead naturally to the definition of a population index of diversity. A means of estimating the values of the model will also be given.

Keywords

MARKOV CHAINSBEHAVIOR INTERACTIONDIVERSITY INDEXDENSITY ESTIMATIONREGULAR SEMIGROUP
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 492 - 500
Copyright
Copyright © Applied Probability Trust 1988 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Allen, B. (1982) A stochastic interactive model for the diffusion of information. J. Math. Sociol. 8, 265–281.Google Scholar
[2] Brumelle, S. and Gerchak, Y. (1980) A stochastic model allowing interaction among individuals and its behavior for large populations. J. Math. Sociol. 7, 73–90.Google Scholar
[3] Clifford, A. and Preston, G. (1961) The Algebraic Theory of Semigroups, Vols. I and II. Amer. Math. Soc., Providence, RI.Google Scholar
[4] Cerrito, P. (1988) Limits of convolution iterates and properties of random walks defined on regular semigroups with applications to matrix semigroups. J. Math. Anal. Appl.Google Scholar
[5] Cerrito, P. (1988) A complete characterization of stochastic processes defined on regular semigroups with applications to stochastic models. Submitted.Google Scholar
[6] Cerrito, P. (1988) Density estimation applied to stochastic abundance models. Submitted.Google Scholar
[7] Conlisk, J. (1978) A stability theorem for an interactive Markov chain. J. Math. Sociol. 6, 163–168.Google Scholar
[8] Engen, S. (1978) Stochastic Abundance Models. Chapman and Hall, London.Google Scholar
[9] Lehoczky, J. (1980) Approximations for interactive Markov chains in discrete and continuous time. J. Math. Sociol. 7, 139–157.Google Scholar
[10] Mukherjea, A. and Tserpes, N. (1976) Measures on Topological Semigroups. Lecture Notes in Mathematics 547, Springer-Verlag, Berlin.Google Scholar
[11] Petrich, M. (1984) Inverse Semigroups. Wiley, New York.Google Scholar
[12] Rao, P. (1983) Nonparametric Functional Estimation. Academic Press, New York.Google Scholar