Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/43662
comunitat-uji-handle3:10234/43643
comunitat-uji-handle4:
INVESTIGACIONMetadatos
Título
Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functionsFecha de publicación
2019-07-16Editor
Texas State UniversityISSN
1072-6691Cita bibliográfica
Calatayud, J., Cortes, J. C., & Jornet, M. (2019). Approximate solutions of randomized non-autonomous complete linear differential equations via probability density functions.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://ejde.math.txstate.edu/Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
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. ... [+]
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-Lo`eve 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. [-]
Publicado en
Electronic Journal of Differential Equations, Vol. 2019, no. 85 (2019)Entidad financiadora
Ministerio de Economía y Competitividad | Universitat Politècnica de València
Código del proyecto o subvención
MTM2017–89664–P
Título del proyecto o subvención
Programa de Ayudas de Investigación y Desarrollo (PAID)
Derechos de acceso
© 2019 Texas State University
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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