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On stochastic growth processes with application to stochastic logistic growth. (English) Zbl 0822.60078
Summary: We develop a general theory for some non-homogeneous density-dependent birth-death processes with special applications to stochastic logistic growth. Approximations to the mean and variance of the logistic process are derived. It is shown that these processes can be closely approximated by diffusion processes. Using this method, new results are developed for approximating the absorption probabilities and the moments of first absorption times for the logistic process.

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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