Abstract
The Malthus process of population growth is reformulated in terms of the probability [Formula: see text] to find exactly [Formula: see text] individuals at time [Formula: see text] assuming that both the birth and the death rates are linear functions of the population size. The master equation for [Formula: see text] is solved exactly. It is shown that [Formula: see text] strongly deviates from the Poisson distribution and is expressed in terms either of Laguerre’s polynomials or a modified Bessel function. The latter expression allows for considerable simplifications of the asymptotic analysis of [Formula: see text].
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