标题： 通过测试函数估计种群年龄依赖过程中的速率 显示英文标题

标题： Estimation of rates in population-age-dependent processes by means of test functions

摘要： 本文旨在开发作者在\cite{FanEtal20}中提出的高度技术性测度值种群模型的实际应用。 我们考虑在一般年龄和种群依赖模型中参数估计的问题，其中个体的出生和死亡率不仅取决于个体的年龄，还取决于整个种群的组成。 我们基于在大承载能力种群中的函数大数定律和中心极限定理中使用测试函数，推导出新的速率估计量。 我们考虑速率是简单的函数，在年龄$x$和测度$A$中取有限多个值，这导致线性方程组。 使用测试函数进行估计的所提出方法是一种根本性的新方法，可以应用于动态系统的广泛模型。 显示英文摘要

摘要： This paper aims to develop practical applications of the model for the highly technical measure-valued populations developed by the authors in \cite{FanEtal20}. We consider the problem of estimation of parameters in the general age and population-dependent model, in which the individual birth and death rates depend not only on the age of the individual but also on the whole population composition. We derive new estimators of the rates based on the use of test functions in the functional Law of Large Numbers and Central Limit Theorem for populations with a large carrying capacity. We consider the rates to be simple functions, that take finitely many values both in age $x$ and measure $A$, which leads to systems of linear equations. The proposed method of using test functions for estimation is a radically new approach which can be applied to a wide range of models of dynamical systems.