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Abstract
Some problems arising when modeling population dynamics by means of stochastic difference and differential equations are discussed. For a particular parametrization of logistic growth equations limit diffusion processes are constructed and interpreted in the light of the Ito-Stratonovich controversy. An indirect confirmation of the validity of May's conjecture on the persistence of a population in a randomly varying environment is also obtained. An extension of these results to a wider class of growth equations is finally provided.
