Convergence of the age structure of general schemes of population processes
| Autor: | Kais Hamza, Fima C. Klebaner, Jie Yen Fan, Peter Jagers |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
education.field_of_study Weak convergence 010102 general mathematics Population Probability (math.PR) central limit theorem 01 natural sciences age-structure dependent population processes Stochastic partial differential equation 010104 statistics & probability Law of large numbers Convergence (routing) carrying capacity FOS: Mathematics Carrying capacity Applied mathematics Limit (mathematics) 0101 mathematics education Mathematics - Probability Mathematics Central limit theorem |
| Zdroj: | Bernoulli 26, no. 2 (2020), 893-926 |
| DOI: | 10.48550/arxiv.1702.08592 |
| Popis: | We consider a family of general branching processes with reproduction parameters depending on the age of the individual as well as the population age structure and a parameter $K$, which may represent the carrying capacity. These processes are Markovian in the age structure. In a previous paper (Proc. Steklov Inst. Math. 282 (2013) 90–105), the Law of Large Numbers as $K\to \infty $ was derived. Here we prove the central limit theorem, namely the weak convergence of the fluctuation processes in an appropriate Skorokhod space. We also show that the limit is driven by a stochastic partial differential equation. |
| Databáze: | OpenAIRE |
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