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Some generalizations of Bailey's birth death and migration model

Some results for a general Markov branching-diffusion process are presented, and applied to a model recently considered by Bailey. Moments of the limiting distributions of certain natural measures of the spatial location and dispersion of the population are shown to be expressible in terms of the Lauricella F D -type hypergeometric functions, when the population multiplies according to the simple birth and death process with λ > μ.