Study of non-homogeneous linear second-order discrete dynamical systems with uncertainties: solution and stability with applications
[EN] We study, from a probabilistic standpoint, a full randomization of nonhomogeneous second-order linear difference equations assuming that its data (initial conditions, coefficients, and forcing term) are random variables. Our analysis consists of computing the so-called first probability density...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/220388 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/220388 |
| Access Level: | acceso abierto |
| Palabra clave: | Random second order linear difference equations Probability density function Random variable transformation technique Random stability Uncertainty quantification Mathematical modeling in biomathematics |
| Sumario: | [EN] We study, from a probabilistic standpoint, a full randomization of nonhomogeneous second-order linear difference equations assuming that its data (initial conditions, coefficients, and forcing term) are random variables. Our analysis consists of computing the so-called first probability density function of the solution, which is a stochastic process, and then analyzing the stability of the solution assuming that all data have an arbitrary joint probability density function. To achieve these goals, we take extensive advantage of the so-called random variable transformation technique. The theoretical results extend their deterministic counterpart, and then, they have many applications in real-world problems where uncertainty plays a key role. Our findings are first illustrated by means of several numerical examples, where different simulations are carried out, and, second, by means of a model belonging to biomathematics. |
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