A developed solution of the stochastic Milne problem using probabilistic transformations

Applied Mathematics Letters

et al. 2014

Section: Examplesmentioning

confidence: 88%

“…method is a powerful technique. This method has been used to study relevant continuous models [9,8,5,10,4]. In this paper we will determine the 1-p.d.f.…”

Section: Motivationmentioning

confidence: 99%

Probabilistic solution of random homogeneous linear second-order difference equations

Applied Mathematics Letters

et al. 2014

“…method has been recently applied in order to determine the 1-p.d.f. of random ordinary differential equations [6,7], random partial differential equations [8,9,10,11] and random difference equations [12]. In [13], a number of illustrative examples show that R.V.T.…”

Section: Motivationmentioning

confidence: 99%

Probabilistic solution of random SI-type epidemiological models using the Random Variable Transformation technique

Communications in Nonlinear Science and Numerical Simulation

et al. 2015

This paper presents a full probabilistic description of the solution of random SI-type epidemiological models which are based on nonlinear differential equations. This description consists of determining: the first probability density function of the solution in terms of the density functions of the diffusion coefficient and the initial condition, which are assumed to be independent random variables; the expectation and variance functions of the solution as well as confidence intervals and, finally, the distribution of time until a given proportion of susceptibles remains in the population. The obtained formulas are general since they are valid regardless the probability distributions assigned to the random inputs. We also present a pair of illustrative examples including in one of them the application of the theoretical results to model the diffusion of a technology using real data.

“…In the context of random differential equations, a number of contributions have dealt with the computation of the 1-PDF in specific problems appearing in physics [15][16][17] or in mathematics [18,19]. A comprehensive study for the random first-order linear differential equation under general hypotheses has been recently published by the authors of [20].…”

Section: Introductionmentioning

confidence: 99%

Random First-Order Linear Discrete Models and Their Probabilistic Solution: A Comprehensive Study

Abstract and Applied Analysis

et al. 2016

This paper presents a complete stochastic solution represented by the first probability density function for random first-order linear difference equations. The study is based on Random Variable Transformation method. The obtained results are given in terms of the probability density functions of the data, namely, initial condition, forcing term, and diffusion coefficient. To conduct the study, all possible cases regarding statistical dependence of the random input parameters are considered. A complete collection of illustrative examples covering all the possible scenarios is provided.