Boundedness analysis of stochastic pantograph differential systems

Stability with general decay rate of hybrid neutral stochastic pantograph differential equations driven by Lévy noise

“…Stochastic pantograph differential equations (SPDEs) with unbounded delay are a class of special SDDEs and the theories of SPDEs including convergence, boundedness, and stability have drawn increasing attention (see, e.g., [36,21,1,4,7,19,41,38,42,5,37,11,20]). For example, Zhang et al [42] discussed the convergence and mean-square stability for the numerical solutions of nonlinear SPDEs.…”

“…Fan et al [5] considered the αth moment asymptotic stability for the exact and numerical solutions of nonlinear SPDEs through the Razumikhin technique. Xu and Hu [37] probed the pth moment exponential ultimate boundedness for SPDEs via the Lyapunov functions and algebraic inequality techniques. Hu et al [11] explored the existence-uniqueness, asymptotic boundedness, along with the exponential stability for the global solution of SPDEs driven by G-Brownian motion.…”