Abstract
In this article, we discuss a class of impulsive stochastic function differential equations driven by $G $-Brownian motion with delayed impulsive effects ($G $-DISFDEs, in short). Some sufficient conditions for $p$-th moment exponential stability of $G $-DISFDEs are derived by means of $G $-Lyapunov function method, average impulsive interval approach and Razumikhin-type conditions. An example is provided to show the effectiveness of the theoretical results.
Highlights
Impulsive dynamical systems have been widely used in many branches of science and technology such as in the transmission of the impulse information, control systems with communication constraints etc
Under the framework of the nonlinear G-expectation, Peng [12, 13] introduced the G-Gaussian distribution and the G-Brownian motion, which have very rich and interesting new structures which nontrivially generalize the classical ones. Since these notions were introduced, many investigators have studied the properties on G-Brownian motion and stochastic differential equation driven by G-Brownian motion (G-SDEs, in short)
Motivated by the aforementioned works, we aim to study the stability problem of stochastic function differential equations driven by G-Brownian motion with delayed
Summary
Impulsive dynamical systems have been widely used in many branches of science and technology such as in the transmission of the impulse information, control systems with communication constraints etc. Under the framework of the nonlinear G-expectation, Peng [12, 13] introduced the G-Gaussian distribution and the G-Brownian motion, which have very rich and interesting new structures which nontrivially generalize the classical ones. Since these notions were introduced, many investigators have studied the properties on G-Brownian motion (see Hu et al [4, 5, 6]) and stochastic differential equation driven by G-Brownian motion (G-SDEs, in short). G-Brownian motion, G-Lyapunov function, delayed impulses, average impulsive interval, exponential stability.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
