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

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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 \({{L}}^2 \) 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.

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Acknowledgements

The authors would like to thank the anonymous referee for careful reading and valuable comments that led to improvement of this work.

This work was partially supported by NSF of China (No.11871476) and NSF of Hunan Province (No. 2019JJ40356).

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  1. Department of Mathematics and Statistics, Central South University, Changsha, China

    Junxia Duan & Jun Peng

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  1. Junxia Duan
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  2. Jun Peng
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Correspondence to Jun Peng.

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Duan, J., Peng, J. An Approximation Scheme for Reflected Stochastic Differential Equations with Non-Lipschitzian Coefficients. J Theor Probab 35, 575–602 (2022). https://doi.org/10.1007/s10959-020-01052-7

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  • DOI: https://doi.org/10.1007/s10959-020-01052-7

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