Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T12:17:11.183Z Has data issue: false hasContentIssue false
  • English
  • Français

On competition between two species

Published online by Cambridge University Press:  14 July 2016

C. J. Ridler-Rowe
C. J. Ridler-Rowe*
Affiliation:
Imperial College London
Get access Rights & Permissions [Opens in a new window]

Abstract

A stochastic model for the competition between two species is considered and a limit theorem is obtained for the size of the surviving species. A limit theorem is also obtained for the probability that a given species should survive the other.

Keywords

MARKOV POPULATION PROCESSCOMPETITION PROCESSCENTRAL LIMIT THEOREMWEAK CONVERGENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 457 - 465
Copyright
Copyright © Applied Probability Trust 1978 

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

Barbour, A. D. (1976) Quasi-stationary distributions in Markov population processes. Adv. Appl. Prob. 8, 296–314.CrossRefGoogle Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Chung, K. L. (1967) Markov Chains with Stationary Transition Probabilities 2nd edn., Springer-Verlag, Berlin.Google Scholar
Kurtz, T. G. (1971) Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Prob. 8, 344–356.Google Scholar
Reuter, G. E. H. (1961) Competition processes. Proc. 4th Berkeley Symp. Math. Statist. Prob. 2, 421–430.Google Scholar
Ridler-Rowe, C. J. (1964) Some Two-Dimensional Markov Processes. Ph.D. Thesis, University of Durham.Google Scholar
Ridler-Rowe, C. J. (1967) On a stochastic model of an epidemic. J. Appl. Prob. 4, 19–33.Google Scholar