First-order linear differential equations whose data are complex random variables: Probabilistic solution and stability analysis via densities
| Autor: | n, Valencia, Spain, Juan Carlos Cortés, José Vicente Romero, Ana Navarro-Quiles, M.-D. Roselló |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Equilibrium point
complex differential equations with uncertainties uncertainty quantification General Mathematics random models Probabilistic logic Probability density function random variable transformation method Stability (probability) Transformation (function) Linear differential equation probability density function QA1-939 Applied mathematics Initial value problem MATEMATICA APLICADA Random variable Mathematics |
| Zdroj: | AIMS Mathematics, Vol 7, Iss 1, Pp 1486-1506 (2022) |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2022088?viewType=HTML |
| Popis: | [EN] Random initial value problems to non-homogeneous first-order linear differential equations with complex coefficients are probabilistically solved by computing the first probability density of the solution. For the sake of generality, coefficients and initial condition are assumed to be absolutely continuous complex random variables with an arbitrary joint probability density function. The probability of stability, as well as the density of the equilibrium point, are explicitly determined. The Random Variable Transformation technique is extensively utilized to conduct the overall analysis. Several examples are included to illustrate all the theoretical findings. This work has been supported by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant PID2020-115270GB-I00 and Generalitat Valenciana (Grant AICO/2021/302). |
| Databáze: | OpenAIRE |
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