Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T05:36:22.737Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-negative matrices, dynamic programming and a harvesting problem

Published online by Cambridge University Press:  14 July 2016

D. R. Grey
D. R. Grey*
Affiliation:
University of Sheffield
*
∗Postal address: Department of Probability and Statistics, The University, Sheffield S3 7RH, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

Existing results on the asymptotic behaviour of solutions to two dynamic programming equations involving non-negative matrices are reviewed and strengthened in certain directions. The results are then applied to strategies for harvesting of a small population so as to optimise its survival potential in a limited environment.

Keywords

MARKOV DECISION PROCESSGALTON-WATSON BRANCHING PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 685 - 694
Copyright
Copyright © Applied Probability Trust 1984 

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

Bellman, R. (1956) On a quasi-linear equation. Canad. J. Math. 8, 198–202.Google Scholar
Bellman, R. (1957) Dynamic Programming. Princeton University Press, Princeton, N.J. Google Scholar
Goodman, D. (1980) Demographic intervention for closely managed populations. In Conservation Biology, ed. Soulé, M. E. and Wilcox, B. A. Sinauer, Sunderland, Mass.Google Scholar
Kennedy, D. P. (1978) On sets of countable non-negative matrices and Markov decision processes. Adv. Appl. Prob. 10, 633–646.Google Scholar
Mandl, P. and Seneta, E. (1969) The theory of non-negative matrices in a dynamic programming problem. Austral. J. Statist. 11, 85–96.Google Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
Rothblum, U. G. and Whittle, P. (1982) Growth optimality for branching Markov decision chains. Math. Operat. Res. 7, 582–601.Google Scholar
Seneta, E. (1973) Non-Negative Matrices. Allen and Unwin, London.Google Scholar
Sladký, K. (1980) Bounds on discrete dynamic programming recursions I. Kybernetika 16, 526–547.Google Scholar
Taylor, H. M., Gourley, R. S., Lawrence, C. E. and Kaplan, R. S. (1974) Natural selection of life history attributes: an analytical approach. Theoret. Popn Biol. 5, 104–122.CrossRefGoogle ScholarPubMed