Lp-calculus Approach to the Random Autonomous Linear Differential Equation with Discrete Delay
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/43662
comunitat-uji-handle3:10234/43643
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https://doi.org/10.1007/s00009-019-1370-6 |
Metadades
Títol
Lp-calculus Approach to the Random Autonomous Linear Differential Equation with Discrete DelayData de publicació
2019-06-19Editor
Springer Nature Switzerland AGISSN
1660-5454; 1660-5446Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://link.springer.com/article/10.1007/s00009-019-1370-6Versió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
In this paper, we provide a full probabilistic study of the random autonomous linear differential equation with discrete delay τ > 0:
x
(t) = ax(t) + bx(t − τ ), t ≥ 0, with initial condition x(t) = g(t),
−τ ≤ t ≤ ... [+]
In this paper, we provide a full probabilistic study of the random autonomous linear differential equation with discrete delay τ > 0:
x
(t) = ax(t) + bx(t − τ ), t ≥ 0, with initial condition x(t) = g(t),
−τ ≤ t ≤ 0. The coefficients a and b are assumed to be random variables, while the initial condition g(t) is taken as a stochastic process.
Using Lp-calculus, we prove that, under certain conditions, the deterministic solution constructed with the method of steps that involves
the delayed exponential function is an Lp-solution too. An analysis of
Lp-convergence when the delay τ tends to 0 is also performed in detail. [-]
Publicat a
Mediterranean Journal of Mathematics, Vol. 16 (2019)Entitat finançadora
Ministerio de Economía y Competitividad (MINECO) | Universitat Politècnica de València
Codi del projecte o subvenció
MTM2017–89664–P
Títol del projecte o subvenció
Programa de Ayudas de Investigación y Desarrollo (PAID)
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© Springer Nature Switzerland AG 2019
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