Stability results for neutral stochastic functional differential equations via fixed point methods

In this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential systems with variable delays by using a contraction mapping principle. Namely, a necessary and sufficient condition ensuring the asymptotic stability is proved. The assumption do...

Descripción completa

Detalles Bibliográficos
Autores: Benhadri, Mimia, Caraballo Garrido, Tomás, Zeghdoudi, Halim
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2020
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/100796
Acceso en línea:https://hdl.handle.net/11441/100796
https://doi.org/10.1080/00207179.2018.1530431
Access Level:acceso abierto
Palabra clave:Fixed points theory
Asymptotic stability in mean square
Neutral stochastic differential equations
Variable delays
Descripción
Sumario:In this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential systems with variable delays by using a contraction mapping principle. Namely, a necessary and sufficient condition ensuring the asymptotic stability is proved. The assumption does not require neither boundedness or differentiability of the delay functions, nor do they ask for a fixed sign on the coefficient functions. In particular, the results improve some previous ones proved by Guo, Y., Xu, C., & Wu, J. [(2017). Stability analysis of neutral stochastic delay differential equations by a generalisation of Banach’s contraction principle. International Journal of Control, 90, 1555–1560]. Finally, an example is exhibited to illustrate the effectiveness of the proposed results.