Perturbed Impulsive Neutral Stochastic Functional Differential Equations

Cheng, Lijuan ^[1] ; Hu, Lanying ^[2] ; Ren, Yong ^[2]
1. [1] Lingnan Normal University
  
  Lingnan Normal University
  
  China
2. [2] Anhui Normal University
  
  Anhui Normal University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 2, 2021
Idioma: inglés
Enlaces
- Texto completo
Resumen
- This paper studies the asymptotic behavior of the mild solution for a class of perturbed impulsive neutral stochastic functional differential equations driven by fractional Brownian motion in Hilbert space. We establish the conditions under which the mild solutions of perturbed impulsive neutral stochastic functional differential equation and the unperturbed one are close on finite time interval when the perturbation tends to zero. Moreover, we show the result holds on time interval whose length tends to infinity as the perturbation tends to zero. As an application, the asymptotic behavior of the mild solution for a class of perturbed impulsive neutral stochastic partial differential equations driven by fractional Brownian motion in Hilbert space is proposed to show the feasibility of the obtained result.