Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-10T21:14:58.660Z Has data issue: false hasContentIssue false
  • English
  • Français

Infinitely divisible random transition probabilities with application to dependent Markov chains

Published online by Cambridge University Press:  17 February 2009

Peter L. Chesson
Peter L. Chesson
Affiliation:
Department of Zoology, The Ohio State University, 1735 Neil Avenue, Columbus, Ohio 43210, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Random transition probability matrices with stationary independent factors define “white noise” environment processes for Markov chains. Two examples are considered in detail. Such environment processes can be used to construct several Markov chains which are dependent, have the same transition probabilities and are jointly a Markov chain. Transition rates for such processes are evaluated. These results have application to the study of animal movements.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 4 , April 1984 , pp. 463 - 472
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Breiman, L., Probability (Addison-Wesley, Reading, Mass., 1968).Google Scholar
[2]Chesson, P. L., “Models for animal movements”, Ph.D. Thesis, University of Adelaide, 1976.Google Scholar
[3]Chesson, P. L., “A theory of animal movements” (1982) (in preparation).Google Scholar
[4]Feller, W., An introduction to probability theory and its applications, Vol. 2 (Wiley, New York, 1971).Google Scholar
[5]Goodman, G. S., “An intrinsic time for non-stationary finite Markov chains”, Z. Wahrsch. Verw. Gebiete 16 (1970), 165–180.CrossRefGoogle Scholar
[6]Hida, T., Stationary stochastic processes (Princeton Univ. Press, Princeton, N. J., 1970).Google Scholar
[7]Keiding, N., “Extinction and exponential growth in random environments”, Theoret. Population Biol. 8 (1975), 49–63.CrossRefGoogle ScholarPubMed
[8]Kingman, J. F. C., “The imbedding problem for finite Markov chains”, Z. Wahrsch. Verw. Gebiete 1 (1962), 14–24.CrossRefGoogle Scholar
[9]May, R. M., Stability and complexity in model ecosystems (Princeton Univ. Press, Princeton, N. J., 2nd edition, 1974).Google Scholar
[10]Nelson, E., “A functional calculus using singular Laplace integrals”, Trans. A mer. Math. Soc. 88 (1958), 400–413.CrossRefGoogle Scholar
[11]Saunders, R., “Conservative processes with stochastic rates”, J. Appl. Probab. 12 (1975), 447–456.CrossRefGoogle Scholar
[12]Saunders, R., “On joint exchangeability and conservative processes with stochastic rates”, J. Appl. Probab. 13 (1976), 584–590.CrossRefGoogle Scholar