Random sums and partially observed branching processes

Source of Publication

Journal of Applied Statistical Science


© Nova Science Publishers, Inc. In the paper we consider a random sum of a double array of independent random variables. We provide limit theorems for the joint distribution of the random sum and the number of summands in various assumptions on the asymptotic behavior of the number of terms. Further, we apply these limit theorems in study of the following modification of a discrete-time branching process. In each generation a binomially distributed subset of the population will be observed. The number of observed individuals constitute a partially observed branching process. After inspection both observed and unobserved individuals change their offspring distributions. Using our limit theorems for the random sum we derive asymptotic distributions for the vector of inspected and partially observed branching processes in cases when the inspected process is subcritical, critical and supercritical.

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Author First name, Last name, Institution

I. Rahimov, Zayed University

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