Applying the random variable transformation method to solve a class of random linear differential equation with discrete delay

Tomás Caraballo, J.-C. Cortés and A. Navarro-Quiles

Applied Mathematics and Computation, 2019, vol. 356, issue C, 198-218

Abstract: We randomize the following class of linear differential equations with delay, xτ′(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.

Keywords: Random linear differential equation with delay; Probability density function; Random variable transformation technique (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319302553
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:356:y:2019:i:c:p:198-218

DOI: 10.1016/j.amc.2019.03.048

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().