Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps

Abstract

The exponential stability of trivial solution and the numerical solution for neutral stochastic functional differential equations (NSFDEs) with jumps is considered. The stability includes the almost sure exponential stability and the mean-square exponential stability. New conditions for jumps are proposed by means of the Borel measurable function to ensure stability. It is shown that if the drift coefficient satisfies the linear growth condition, the Euler-Maruyama method can reproduce the corresponding exponential stability of the trivial solution. A numerical example is constructed to illustrate our theory

Sharp Threshold for the Dynamics of a SIRS Epidemic Model With General Awareness- Induced Incidence and Four Independent Brownian Motions

“…In this section, we provide three numerical simulation results for the stochastic model(2) to substantiate theoretical findings: threshold theorem in section 3 and persistence theorem in section 4. Using Milstein's higher order method [22], [23], the numerical equations are…”

Delay‐dependent stability of highly nonlinear neutral stochastic functional differential equations

“…Recently, there was a great deal of attention to the stability of neutral stochastic differential equations (NSDEs) (see, e.g., related works [22][23][24][25][26][27][28][29][30][31] ). One of the important classes of NSDEs is the class of neutral stochastic functional differential equations (NSFDEs).…”

Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays

“…Many stochastic systems which not only depend on present and past states but also involve derivatives with delays are modeled by neutral stochastic differential delay equations (NSDDEs). Although extensive literature can be found in this area, we mention a few of them herein [16][17][18][19][20][21][22][23]. Also, many researchers have made efforts in regard to the stability of highly nonlinear neutral stochastic systems.…”