Stability analysis of theθ-method for hybrid neutral stochastic functional differential equations with jumps

A Note on Exponential Stability for Numerical Solution of Neutral Stochastic Functional Differential Equations

“…As an important type of SDEs, NSFDEs do not have explicit solutions, and we have found content with an approximation via a numerical approach. In recent years, some numerical schemes such as the EM method [12], tamed EM method [13], and stochastic θ method [14] have been proposed to discuss the convergence and the stability analysis for a numerical solution of NSFDEs. In [12], Wu and Mao discussed the convergence of the EM numerical solution for NSFDEs.…”

“…In [13], Deng et al proposed two types of explicit tamed EM schemes for NSFDEs with superlinearly growing drift and diffusion coefficients to analyze the exponential stability in moment for the numerical solution. In [14], Li and Yang studied the exponential stability in moment and the almost surely exponential stability of the EM numerical solution of NSFDEs with jumps.…”