>The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. T'/> (CMMSE2018 paper) Solving the random Pielou logistic equation with the random variable transformation technique: Theory and applications
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(CMMSE2018 paper) Solving the random Pielou logistic equation with the random variable transformation technique: Theory and applications

机译:(CMMSE2018纸)用随机变换技术解决随机PIELOU物流方程:理论与应用

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>The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However, discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state, and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples: The first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data.
机译: >通过数学建模的群体大小的动态研究是一个兴趣和广泛研究的问题。传统上,基于微分方程的连续确定方法已经用于处理这个问题。但是,某些型号的离散版本也是可用的,有时更加充分。在本文中,我们随机化了pielou逻辑方程,以包括建模中固有的不确定性。利用随机变量的转换方法,我们通过计算随机随机过程的概率密度函数,稳态和时间达到一定程度的群体的概率密度函数来提供完全概率描述。到达了。理论结果通过两个示例说明:第一个由数值实验组成,第二个是使用真实数据研究技术扩散的应用。

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