Article
Applying the random variable transformation method to solve a class of random linear differential equation with discrete delay
Author/s | Caraballo Garrido, Tomás
Cortés López, Juan Carlos Navarro Quilés, Ana |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2019-09-01 |
Deposit Date | 2019-04-12 |
Published in |
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Abstract | We randomize the following class of linear differential equations with delay, x 0 τ (t) = axτ(t) + bxτ(t − τ), t > 0, and initial condition, xτ(t) = g(t), −τ ≤ t ≤ 0, by assuming that coefficients a and b are random variables ... We randomize the following class of linear differential equations with delay, x 0 τ (t) = axτ(t) + bxτ(t − τ), t > 0, and initial condition, xτ(t) = g(t), −τ ≤ t ≤ 0, by assuming that coefficients a and b are random variables and the initial condition g(t) is a stochastic process. We consider two cases, depending on the functional form of the stochastic process g(t), and then we solve, from a probabilistic point of view, both random initial value problems by determining explicit expressions to the first probability density function, f(x, t; τ), of the corresponding solution stochastic processes. Afterwards, we establish sufficient conditions on the involved random input parameters in order to guarantee that f(x, t; τ) converges, as τ → 0 +, to the first probability density function, say f(x, t), of the corresponding associated random linear problem without delay (τ = 0). The paper concludes with several numerical experiments illustrating our theoretical findings. |
Project ID. | MTM2017-89664–P
MTM2015-63723-P P12-FQM-1492 |
Citation | Caraballo Garrido, T., Cortés López, J.C. y Navarro Quilés, 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. |
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