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A diffusion model for population growth in random environment. (English) Zbl 0291.92031


MSC:

92D25 Population dynamics (general)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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References:

[1] Aitchinson, J.; Brown, J. A.C., The Lognormal Distribution (1966), Univ. of Cambridge Press: Univ. of Cambridge Press Cambridge
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[3] Cherkasov, I. D., On transforming the diffusion process to a Wiener process, Teor. Vezoyatnost. i Primenen, 2, 384-388 (1957), (English translation in our possession) · Zbl 0081.13501
[4] Crow, J. F.; Kimura, M., Introduction to Population Genetics Theory (1971), Harper & Row: Harper & Row New York
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[6] Feller, W., Two singular diffusion problems, Ann. of Math, 54, 173-182 (1951) · Zbl 0045.04901
[7] Feller, W., The parabolic differential equations and the associated semigroups of transformations, Ann. of Math, 55, 468-519 (1952) · Zbl 0047.09303
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[9] Levins, R., The effect of random variations of different types on population growth, (Proc. Nat. Acad. Sci, 62 (1969)), 1061-1065
[10] Lewontin, R. C.; Cohen, D., On population growth in randomly varying environment, (Proc. Nat. Ac. Sciences, 62 (1969)), 1056-1060
[11] Stratonovich, R. L., (Topics in the Theory of Random Noise, Vol. I (1963), Gordon and Breach: Gordon and Breach New York)
[12] Stratonovich, R. L., Conditional Markov Processes and their Application to the Theory of Optimal Control (1968), Elsevier: Elsevier New York · Zbl 0159.46804
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