6533b824fe1ef96bd1280b0d

RESEARCH PRODUCT

First-order linear differential equations whose data are complex random variables: Probabilistic solution and stability analysis via densities

NJuan Carlos CortésJosé Vicente RomeroAna Navarro-quilesAna Navarro-quilesM.-d. RosellóM.-d. Roselló

subject

Equilibrium pointcomplex differential equations with uncertaintiesuncertainty quantificationGeneral Mathematicsrandom modelsProbabilistic logicProbability density functionrandom variable transformation methodStability (probability)Transformation (function)Linear differential equationprobability density functionQA1-939Applied mathematicsInitial value problemMATEMATICA APLICADARandom variableMathematicsMathematics

description

[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.

yearjournalcountryeditionlanguage
2022-01-01AIMS Mathematics
10.3934/math.2022088https://www.aimspress.com/article/doi/10.3934/math.2022088?viewType=HTML