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Exponential stability of numerical solution to neutral stochastic functional differential equation

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  • Zhou, Shaobo

Abstract

Stability of the solution to neutral stochastic functional differential equation (NSFDE) has received a great deal of attention, but there is so far little work on stability of numerical solution. To close the gap, the paper develops new criteria on stability of numerical solutions to linear and nonlinear NSFDEs. We show that the backward Euler–Maruyama(EM) method can reproduce the almost surely exponential stability of the exact solution to highly nonlinear NSFDE, and EM method can preserve the almost surely exponential stability of NSFDE with linear growing coefficients. Two examples are provided to illustrate the main results.

Suggested Citation

  • Zhou, Shaobo, 2015. "Exponential stability of numerical solution to neutral stochastic functional differential equation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 441-461.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:441-461
    DOI: 10.1016/j.amc.2015.05.041
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    Cited by:

    1. Chen, Weimin & Zhang, Baoyong & Ma, Qian, 2018. "Decay-rate-dependent conditions for exponential stability of stochastic neutral systems with Markovian jumping parameters," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 93-105.
    2. Tan, Li & Yuan, Chenggui, 2018. "Strong convergence of a tamed theta scheme for NSDDEs with one-sided Lipschitz drift," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 607-623.
    3. Li, Guangjie & Yang, Qigui, 2021. "Stability analysis of the θ-method for hybrid neutral stochastic functional differential equations with jumps," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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