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Optimal control of a birth-and-death process population model. (English) Zbl 0303.60082

MSC:
60J85 Applications of branching processes
60J99 Markov processes
92D25 Population dynamics (general)
93E20 Optimal stochastic control
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[1] Doubleday, W.G., On linear birth-death processes with multiple births, Math. biosci., 17, 43-56, (1973) · Zbl 0258.92007
[2] Tsokos, C.P.; Hinkley, W.S., A stochastic bivariate model for competing species, Math. biosci., 16, 191-208, (1973) · Zbl 0249.92002
[3] Renshaw, E., Birth, death and migration processes, Biometrika, 59, 1, 49-60, (1972) · Zbl 0232.60073
[4] Keyfitz, N., Introduction to the mathematics of population, (1968), Addison Wesley New York, Chapter 16
[5] Sancho, N.G.F., Optimal policies in resource management, Math. biosci., 17, 35-41, (1973) · Zbl 0261.92004
[6] Shoemaker, C., Optimization of agricultural pest management II: formulation of a control model, Math. biosci., 17, 357-365, (1973)
[7] Arley, N., On the general birth-and-death-with-immigration stochastic process, Skandinavisk aktuarietidskrift, 12, 175-182, (1967) · Zbl 0218.60078
[8] Piaggio, H.T.H., An elementary treatise on differential equations and their applications, (1956), Bells Mathematical Series London · Zbl 0001.39902
[9] Takács, L., Introduction to the theory of queues, (1962), Oxford University Press New York · Zbl 0118.13503
[10] Darroch, J.N., The multiple-recapture census. I. estimation of a closed population, Biometrika, 45, 356, (1958) · Zbl 0099.14703
[11] Darroch, J.N., The multiple-recapture census. II. estimation when there is immigration or birth, Biometrika, 46, 336-351, (1959)
[12] Jolly, G.M., Explicit estimate from capture-recapture data with both death and immigration stochastic model, Biometrika, 52, 225-247, (1965) · Zbl 0141.36601
[13] Himmelblau, D.M., Applied nonlinear programming, (1972), McGraw-Hill New York · Zbl 0521.93057
[14] Hadley, G., Nonlinear and dynamic programming, (1964), Addison Wesley New York · Zbl 0179.24601
[15] Meditch, J.S., Stochastic optimal linear estimation and control, (1964), McGraw-Hill New York · Zbl 0225.93045
[16] Nemhauser, G.L., Introduction to dynamic programming, (1966), Wiley New York · Zbl 0139.13202
[17] Bellman, R.E.; Dreyfus, S.E., Applied dynamic programming, (1962), Princeton Univ. Press Princeton · Zbl 0106.34901
[18] Jacobson, D.H.; Mayne, D.Q., Differential dynamic programming, (1970), Elsevier New York, Chapter 4 · Zbl 0223.49022
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