## Abstract

The exponential stability of trivial solution and 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.

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## Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573156, 61503142) and Key Youth Research Fund of Guangdong University of Technology (Grant No. 17ZK0010).

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Mo, H., Li, M., Deng, F. *et al.* Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps.
*Sci. China Inf. Sci.* **61, **70214 (2018). https://doi.org/10.1007/s11432-017-9301-y

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### Keywords

- neutral stochastic functional differential equations with jumps
- almost sure exponential stability
- mean-square exponential stability
- Euler-Maruyama method