Hostname: page-component-788cddb947-jbkpb Total loading time: 0 Render date: 2024-10-09T09:04:55.760Z Has data issue: false hasContentIssue false
  • English
  • Français

A self-excited migration process

Published online by Cambridge University Press:  14 July 2016

A. J. Branford
A. J. Branford*
Affiliation:
University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

Processes whose entities would be independent but whose behaviour is influenced by environmental variables, which they in turn affect, are processes with mediated interactions. The independent open migration process with which is associated a random variable, the excitation, is such a process. This self-excited (conditionally) independent open migration process, with finite excitation, is related to a derived process, its piecewise-deterministic analogue. The correspondence gives insight into the process, as well as an equilibrium independence result. A simple example illustrates the presence of paroxysmal phenomena.

Keywords

EXCITATIONMEDIATED INTERACTIONSOPEN MIGRATION PROCESSPIECEWISE-DETERMINISTIC
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 58 - 67
Copyright
Copyright © Applied Probability Trust 1985 

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

Band, W. (1955) An Introduction to Quantum Statistics. Van Nostrand, Princeton, New Jersey.Google Scholar
Bartlett, M. S. (1978) An Introduction to Stochastic Processes. 3rd edn, Cambridge University Press.Google Scholar
Branford, A. J. (1983) Self-excited Random Processes. Ph.D. Dissertation, Statistical Laboratory, University of Cambridge.Google Scholar
Davis, M. H. A. (1983) Piecewise deterministic Markov processes: a general class of non-diffusion stochastic models. Research Report IC/EE/CON.83.3, Department of Electrical Engineering, Imperial College, London.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, Chichester.Google Scholar
Phillips, O. M. (1973) The equilibrium of simple marine biological systems. I Primary nutrient consumers. Amer. Natur. 107, 73–93.Google Scholar
Phillips, O. M. (1974) The equilibrium of simple marine biological systems. II Herbivores. Arch. Hydrobiol. 73, 310–333.Google Scholar
Tsetlin, M. L. (1973) Automaton Theory and Modeling of Biological Systems. Mathematics in Science and Engineering 102, Academic Press, New York.Google Scholar
Vermes, D. (1983) Optimal control of piecewise deterministic stochastic processes. Research Report IC/EE/CON.83.6, Department of Electrical Engineering, Imperial College, London.Google Scholar
Whittle, P. (1968) Equilibrium distributions for an open migration process. J. Appl. Prob. 5, 567–571.Google Scholar
Whittle, P. (1983) Competition and bottle-necks. In Probability, Statistics and Analysis, ed. Kingman, J. F. C. and Reuter, G. E. H., London Mathematical Society Lecture Note Series 79, Cambridge University Press, 277–284.Google Scholar