Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions
| dc.contributor.author | Calatayud, Julia | |
| dc.contributor.author | Cortes, Juan Carlos | |
| dc.contributor.author | Jornet, Marc | |
| dc.date.accessioned | 2021-11-29T19:54:33Z | |
| dc.date.available | 2021-11-29T19:54:33Z | |
| dc.date.issued | 2019-07-16 | |
| dc.description.abstract | Solving a random differential equation means to obtain an exact or approximate expression for the solution stochastic process, and to compute its statistical properties, mainly the mean and the variance functions. However, a major challenge is the computation of the probability density function of the solution. In this article we construct reliable approximations of the probability density function to the randomized non-autonomous complete linear differential equation by assuming that the diffusion coefficient and the source term are stochastic processes and the initial condition is a random variable. The key tools to construct these approximations are the random variable transformation technique and Karhunen-Loeve expansions. The study is divided into a large number of cases with a double aim: firstly, to extend the available results in the extant literature and, secondly, to embrace as many practical situations as possible. Finally, a wide variety of numerical experiments illustrate the potentiality of our findings. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 40 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Calatayud, J., Cortés, J. C., & Jornet, M. (2019). Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions. <i>Electronic Journal of Differential Equations, 2019</i>(85), pp. 1-40. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14973 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Random non-autonomous complete linear differential equation | |
| dc.subject | Random variable transformation technique | |
| dc.subject | Karhunen-Loeve expansion | |
| dc.subject | Probability density function | |
| dc.title | Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions | |
| dc.type | Article |