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Numerical approximation of nonlinear neutral stochastic functional differential equations

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Abstract

The paper investigates numerical approximations for solution of neutral stochastic functional differential equation (NSFDE) with coefficients of the polynomial growth. The main aim is to develop the convergence in probability of Euler-Maruyama approximate solution under highly nonlinear growth conditions. The paper removes the linear growth condition of the existing results replacing by highly nonlinear growth conditions, so the convergence criteria here may cover a wider class of nonlinear systems. Moreover, we also prove the existence-and-uniqueness of the global solutions for NSFDEs with coefficients of the polynomial growth. Finally, two examples is provided to illustrate the main theory.

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Acknowledgements

The authors express their sincere gratitude to two anonymous referees for their detailed comments and helpful suggestions. The financial support from the National Natural Science Foundation of China (Grant No. 70871046) and Fundamental Research Funds for the Central Universities (2011QN167).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Shaobo Zhou

  2. School of civil Engineering, Wuhan University, Wuhan, 430072, China

    Zheng Fang

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  1. Shaobo Zhou
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  2. Zheng Fang
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Correspondence to Shaobo Zhou.

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Zhou, S., Fang, Z. Numerical approximation of nonlinear neutral stochastic functional differential equations. J. Appl. Math. Comput. 41, 427–445 (2013). https://doi.org/10.1007/s12190-012-0605-5

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  • DOI: https://doi.org/10.1007/s12190-012-0605-5

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