Applying the Random Variable Transformation method to solve a class of random linear differential equation with discrete delay

Abstract

[EN] We randomize the following class of linear differential equations with delay, x(tau)' (t) = ax(tau) (t) bx(tau) (t -tau), t> 0, and initial condition, x(tau )(t) = g(t), -tau 0(+), to the first probability density function, say f(x, t), of the corresponding associated random linear problem without delay (tau = 0). The paper concludes with several numerical experiments illustrating our theoretical findings.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2017-89664-P and MTM2015-63723-P and Junta de Andalucia under Proyecto de Excelencia P12-FQM-1492. Ana Navarro Quiles acknowledges the Fundacio Ferran Sunyer i Balaguer and the Instituto de Estudios Catalanes for its contribution through the Borsa Ferran Sunyer i Balaguer. Ana Navarro Quiles acknowledges the postdoctoral contract financed by DyCon project funding from the European Research Council(ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No 694126-DYCON). The authors express their deepest thanks and respect to the editors and reviewers for their valuable comments.Caraballo, T.; Cortés, J.; Navarro-Quiles, A. (2019). Applying the Random Variable Transformation method to solve a class of random linear differential equation with discrete delay. Applied Mathematics and Computation. 356:198-218. https://doi.org/10.1016/j.amc.2019.03.048S19821835