Abstract
A sequence of density-dependent analogues of continuous time branching processes is shown to converge weakly to a diffusion. The diffusion has infinitesimal mean displacement (drift) λxα(x) and infinitesimal variance 2λxβ, where λ and β are positive constants and α is a bounded, continuous, real-valued function on [0,∞). Boundary behavior of the diffusion is studied, in the case where α(x) is negative for large enough x values. This corresponds to a “controlled” population in which growth is retarded when the population is too large.
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Wofsy, C. (1980). Behavior of Limiting Diffusions for Density-Dependent Branching processes. In: Jäger, W., Rost, H., Tautu, P. (eds) Biological Growth and Spread. Lecture Notes in Biomathematics, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61850-5_13
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DOI: https://doi.org/10.1007/978-3-642-61850-5_13
Publisher Name: Springer, Berlin, Heidelberg
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