Limit Theorems for Branching Processes with Random Migration Stopped at Zero
In this paper, we study a generalization of the classical BienayméGalton-Watson branching process by allowing a random migration component stopped at zero (i.e. the state zero is absorbing). In each generation for which the population size is positive, with probability p two types of emigration are available - a random number of offsprings and a random number of families (these two random variables can be dependent); with probability q there is not any migration; with probability r an immigration of new individuals is possible, p+q+r = 1. The critical case is investigated with an extension when the initial law is attracted to a stable (p) law, p ≤ 1. The asymptotic form of the probability of non-extinction is studied and conditional limit theorems for the population size are obtained, depending on the range of an additional parameter of criticality.
Key wordsrandom migration extinction moments conditional limit theorems
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