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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.
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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

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 685 - 694
Copyright
Copyright © Applied Probability Trust 1984 

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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