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An Approximation Scheme for Reflected Stochastic Differential Equations with Non-Lipschitzian Coefficients

Author

Listed:
  • Junxia Duan

    (Central South University)

  • Jun Peng

    (Central South University)

Abstract

In this paper, we study a numerical approximation scheme for reflected stochastic differential equations (SDEs) with non-Lipschitzian coefficients in a bounded convex domain. It is shown, under some mild conditions, that the approximation scheme converges in uniform $${{L}}^2 $$ L 2 to the solution of reflected SDEs. Moreover, we move from local to global monotonicity conditions and consider the rate of convergence for our approximation scheme to reflected SDEs with coefficients which have at most polynomial growth.

Suggested Citation

  • Junxia Duan & Jun Peng, 2022. "An Approximation Scheme for Reflected Stochastic Differential Equations with Non-Lipschitzian Coefficients," Journal of Theoretical Probability, Springer, vol. 35(1), pages 575-602, March.
  • Handle: RePEc:spr:jotpro:v:35:y:2022:i:1:d:10.1007_s10959-020-01052-7
    DOI: 10.1007/s10959-020-01052-7
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    References listed on IDEAS

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    1. Lan, Guangqiang & Wu, Jiang-Lun, 2014. "New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4030-4049.
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