A new order from the combination of exact coupling and the Euler scheme

Yousef Alnafisah; Yousef Alnafisah

doi:10.3934/math.2022353

AIMS Mathematics

2022, Volume 7, Issue 4: 6356-6364. doi: 10.3934/math.2022353

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A new order from the combination of exact coupling and the Euler scheme

Yousef Alnafisah ^,

Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia

Received: 08 September 2021 Revised: 29 December 2021 Accepted: 03 January 2022 Published: 19 January 2022
MSC : 60H10, 60H35

Davie defined a Levy variant and the combination of single random variables to ensure that the diffusion matrix did not degenerate. The use of the method proposed by Davie, which is a combination of the Euler method and the exact combination, was investigated for applying the degenerate Levy diffusion approach to $ \big(B_{ik}(Y)\big) $. We use certain degenerate conditions of diffusion which contribute to order convergence. We also show MATLAB codes to apply the integrated solution to an SDE and observe a convergence behavior. We also evaluate the agreement between the theoretical values and the MATLAB numerical example.
- exact coupling,
- stochastic differential equations (SDE),
- numerical solution of stochastic differential equations,
- strong convergence,
- Euler method
Citation: Yousef Alnafisah. A new order from the combination of exact coupling and the Euler scheme[J]. AIMS Mathematics, 2022, 7(4): 6356-6364. doi: 10.3934/math.2022353

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Abstract

Davie defined a Levy variant and the combination of single random variables to ensure that the diffusion matrix did not degenerate. The use of the method proposed by Davie, which is a combination of the Euler method and the exact combination, was investigated for applying the degenerate Levy diffusion approach to $ \big(B_{ik}(Y)\big) $. We use certain degenerate conditions of diffusion which contribute to order convergence. We also show MATLAB codes to apply the integrated solution to an SDE and observe a convergence behavior. We also evaluate the agreement between the theoretical values and the MATLAB numerical example.

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