arXiv subjects

A. Navarro-Quiles

Publications and source records attributed to A. Navarro-Quiles.

3 recordsLinked to original sources

arXiv2019

A probabilistic analysis of a Beverton-Holt type discrete model: Theoretical and computing analysis

In this paper a randomized version of the Beverton-Holt type discrete model is proposed. Its solution stochastic process and the random steady state are determined. Its first probability density function and second probability density function are obtained by means of the random variable transformation method, providing a full probabilistic description of the solution. Finally, several numerical examples are shown.

math.GM↗

arXiv2019

Analysis of random non-autonomous logistic-type differential equations via the Karhunen-Loève expansion and the Random Variable Transformation technique

This paper deals with the study, from a probabilistic point of view, of logistic-type differential equations with uncertainties. We assume that the initial condition is a random variable and the diffusion coefficient is a stochastic process. The main objective is to obtain the first probability density function, $f_1(p,t)$, of the solution stochastic process, $P(t,ω)$. To achieve this goal, first the diffusion coefficient is represented via a truncation of order $N$ of the Karhunen-Loève expansion, and second, the Random Variable Transformation technique is applied. In this manner, approximations, say $f_1^N(p,t)$, of $f_1(p,t)$ are constructed. Afterwards, we rigorously prove that $f_1^N(p,t) \longrightarrow f_1(p,t)$ as $N\to \infty$ under mild conditions assumed on input data (initial condition and diffusion coefficient). Finally, three illustrative examples are shown.

math.PR↗

arXiv2019

Solving the Random Pielou Logistic Equation with the Random Variable Transformation Technique: Theory and Applications

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.

math.PR↗