Solving random homogeneous linear second-order differential equations: a full probabilistic description
| Autor: | Casabán, M.C., Cortés, J.C., Romero, José-Vicente, Roselló, María-Dolores |
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| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Random variable transformation method
Multivariate random variable General Mathematics 010102 general mathematics Mathematical analysis Random function Random element 010103 numerical & computational mathematics Conditional probability distribution 01 natural sciences Algebra of random variables Algebraic formula for the variance Convergence of random variables Sum of normally distributed random variables Applied mathematics First and second probability density functions 0101 mathematics MATEMATICA APLICADA Random homogeneous linear second-order differential equations Mathematics |
| Zdroj: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname |
| Popis: | [EN] In this paper a complete probabilistic description for the solution of random homogeneous linear second-order differential equations via the computation of its two first probability density functions is given. As a consequence, all unidimensional and two-dimensional statistical moments can be straightforwardly determined, in particular, mean, variance and covariance functions, as well as the first-order conditional law. With the aim of providing more generality, in a first step, all involved input parameters are assumed to be statistically dependent random variables having an arbitrary joint probability density function. Second, the particular case that just initial conditions are random variables is also analysed. Both problems have common and distinctive feature which are highlighted in our analysis. The study is based on random variable transformation method. As a consequence of our study, the well-known deterministic results are nicely generalized. Several illustrative examples are included. This work has been partially supported by the Spanish M. C. Y. T. Grant MTM2013-41765-P. |
| Databáze: | OpenAIRE |
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