Euler-Maruyama approximation of backward doubly stochastic differential delay equations

  • Authors

    • Falah Sarhan School of Mathematics and Statistics, Huazhong University of Science and Technology
    • LIU JICHENG School of Mathematics and Statistics, Huazhong University of Science and Technology
    2016-07-25
    https://doi.org/10.14419/ijamr.v5i3.6358
  • Backward doubly stochastic differential equation, Conditional expectation, Approximation theory, Time delayed coefficients.

  • In this paper, we attempt to introduce a new numerical approach to solve backward doubly stochastic differential delay equation ( shortly-BDSDDEs ). In the beginning, we present some assumptions to get the numerical scheme for BDSDDEs, from which we prove important theorem. We use the relationship between backward doubly stochastic differential delay equations and stochastic controls by interpreting BDSDDEs as some stochastic optimal control problems, to solve the approximated BDSDDEs and we prove that the numerical solutions of backward doubly stochastic differential delay equation converge to the true solution under the Lipschitz condition.

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  • How to Cite

    Sarhan, F., & JICHENG, L. (2016). Euler-Maruyama approximation of backward doubly stochastic differential delay equations. International Journal of Applied Mathematical Research, 5(3), 146-151. https://doi.org/10.14419/ijamr.v5i3.6358