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Abstract and Applied Analysis
Volume 2016, Article ID 6372108, 22 pages
Research Article

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

Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, Building 8G, 2nd Floor, 46022 Valencia, Spain

Received 3 October 2015; Accepted 1 February 2016

Academic Editor: Patricia J. Y. Wong

Copyright © 2016 M.-C. Casabán et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.