The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the probability density function
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/43662
comunitat-uji-handle3:10234/43643
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INVESTIGACIONEste recurso está restringido
https://doi.org/10.1016/j.physa.2018.08.024 |
Metadatos
Título
The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the probability density functionFecha de publicación
2018-08-13Editor
Elsevier B.V.ISSN
0378-4371Cita bibliográfica
Calatayud, J., Cortés, J. C., & Jornet, M. (2018). The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the probability density function. Physica A: Statistical Mechanics and its Applications, 512, 261-279.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.sciencedirect.com/science/article/pii/S0378437118309762?via%3Dihub#d1e711Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
This paper deals with the damped pendulum random differential equation: X¨(t)+2ω0ξX˙(t)
+ ω
2
0
X(t) = Y(t), t ∈ [0, T ], with initial conditions X(0) = X0 and X˙(0) = X1. The
forcing term Y(t) is a stochastic ... [+]
This paper deals with the damped pendulum random differential equation: X¨(t)+2ω0ξX˙(t)
+ ω
2
0
X(t) = Y(t), t ∈ [0, T ], with initial conditions X(0) = X0 and X˙(0) = X1. The
forcing term Y(t) is a stochastic process and X0 and X1 are random variables in a common
underlying complete probability space (Ω, F, P). The term X(t) is a stochastic process that
solves the random differential equation in both the sample path and in the Lp
senses.
To understand the probabilistic behavior of X(t), we need its joint finite-dimensional
distributions. We establish mild conditions under which X(t) is an absolutely continuous
random variable, for each t, and we find its probability density function fX(t)(x). Thus,
we obtain the first finite-dimensional distributions. In practice, we deal with two types
of forcing term: Y(t) is a Gaussian process, which occurs with the damped pendulum
stochastic differential equation of Itô type; and Y(t) can be approximated by a sequence
{YN (t)}
∞
N=1
in L2
([0, T ] × Ω), which occurs with Karhunen–Loève expansions and some
random power series. Finally, we provide numerical examples in which we choose specific
random variables X0 and X1 and a specific stochastic process Y(t), and then, we find the
probability density function of X(t). [-]
Publicado en
Physica A: Statistical Mechanics and its Applications, Vol. 512 (15 December 2018)Entidad financiadora
Ministerio de Ciencia e Innovación | 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
© 2018 Elsevier B.V. All rights reserved.
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