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Numerical approximation of stochastic differential delay equation with coefficients of polynomial growth

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Abstract

Although numerical methods of nonlinear stochastic differential delay equations (SDDEs) have been discussed by several authors, there is so far little work on the numerical approximation of SDDE with coefficients of polynomial growth. The main aim of the paper is to investigate convergence in probability of the Euler-Maruyama (EM) approximate solution for SDDE with one-sided polynomial growing drift coefficient and polynomial growing diffusion coefficient. Moreover, we prove the existence-and-uniqueness of almost surely exponentially stable global solution for this nonlinear stochastic delay system. Finally, a computer simulation confirms the efficiency of our numerical method.

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Acknowledgments

The author expresses her 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.11301198;11422110).

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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 Science, Hubei University of Technology, Wuhan, 430068, China

    Chaozhu Hu

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  1. Shaobo Zhou
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  2. Chaozhu Hu
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Correspondence to Shaobo Zhou.

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Zhou, S., Hu, C. Numerical approximation of stochastic differential delay equation with coefficients of polynomial growth. Calcolo 54, 1–22 (2017). https://doi.org/10.1007/s10092-016-0173-4

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  • DOI: https://doi.org/10.1007/s10092-016-0173-4

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