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

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.