A mean square chain rule and its application in solving the random Chebyshev differential equation
[EN] In this paper a new version of the chain rule for calculat- ing the mean square derivative of a second-order stochastic process is proven. This random operational calculus rule is applied to construct a rigorous mean square solution of the random Chebyshev differential equation (r.C.d.e.) assum...
| Authors: | , , |
|---|---|
| Format: | article |
| Publication Date: | 2017 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/105851 |
| Online Access: | https://riunet.upv.es/handle/10251/105851 |
| Access Level: | Open access |
| Keyword: | Mean square chain rule Random Chebyshev differential equation Mean square and mean fourth calculus Monte Carlo simulations MATEMATICA APLICADA |
| Summary: | [EN] In this paper a new version of the chain rule for calculat- ing the mean square derivative of a second-order stochastic process is proven. This random operational calculus rule is applied to construct a rigorous mean square solution of the random Chebyshev differential equation (r.C.d.e.) assuming mild moment hypotheses on the random variables that appear as coefficients and initial conditions of the cor- responding initial value problem. Such solution is represented through a mean square random power series. Moreover, reliable approximations for the mean and standard deviation functions to the solution stochastic process of the r.C.d.e. are given. Several examples, that illustrate the theoretical results, are included. |
|---|