The implementation of approximate coupling in two-dimensional SDEs with invertible diffusion terms

Abstract

We explain and prove some lemmas of the approximate coupling and we give some details of the Matlab implementation of this method. A particular invertible SDEs is used to show the convergence result for this method for general d, which will give an order one error bounds..

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Acknowledgement

The author would first like to thank Professor Sandy Davie, Professor Istvan Gyongy and Dr Sotirios Sabanis from Edinburgh University for their useful discussions and for their suggestions and improvements to this version of this paper.

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Correspondence to Yousef Alnafisah.

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The author gratefully acknowledge Qassim University, represented by the deanship of scientific research, on the material support for this research under the number (3871-cos-2018-1-14-S) during the academic year 2018.

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Alnafisah, Y. The implementation of approximate coupling in two-dimensional SDEs with invertible diffusion terms. Appl. Math. J. Chin. Univ. 35, 166–183 (2020). https://doi.org/10.1007/s11766-020-3663-8

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Keywords

  • stochastic differential equation
  • milstein method
  • euler method

MR Subject Classification

  • 60H10