Probabilistic analysis of a general class of nonlinear random differential equations with state-dependent impulsive terms via probability density functions

[EN] In this contribution, we rigorously construct a pathwise solution to a general scalar random differential equation with state-dependent Dirac-delta impulse terms at a finite number of time instants. Furthermore, we obtain the first probability density function of the solution by combining two m...

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Detalles Bibliográficos
Autores: Bevia, Vicente J., Jornet-Sanz, Marc, Cortés, J.-C.|||0000-0002-6528-2155, Villanueva Micó, Rafael Jacinto|||0000-0002-0131-0532
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/203297
Acceso en línea:https://riunet.upv.es/handle/10251/203297
Access Level:acceso abierto
Palabra clave:Random differential equations
Dirac-delta impulse terms
First probability density function
Liouville-Gibbs equation
Random variable transformation technique
MATEMATICA APLICADA
Descripción
Sumario:[EN] In this contribution, we rigorously construct a pathwise solution to a general scalar random differential equation with state-dependent Dirac-delta impulse terms at a finite number of time instants. Furthermore, we obtain the first probability density function of the solution by combining two main results, firstly, the Liouville-Gibbs equation between the impulse instants, and secondly, the Random Variable Transformation technique at the impulse times. Finally, all theoretical findings are illustrated on two stochastic models, widely used in mathematical modeling, carrying on computational simulations.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).