Yousef Alnafisah and Hamdy M. Ahmed. An Experimental Implementation for Stochastic Differential Equation Using the Exact Coupling with Non-Degeneracy Diffusion. Dynamic Systems and Applications 30 (2021) No.7, 1105-1115

https://doi.org/10.46719/dsa20213073

ABSTRACT.
Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multi-dimensional. In this paper, we show by the Matlab implementation an order one error bounds for Davie’s scheme (Davie, 2015) in section (8) for the Lp space assuming the invertibility of the diffusion matrix. We give a numerical example to show the convergence behavior for 2-dimensional SDE using an explicit
version for the coefficients.

AMS Subject Classication: 60H10. Keywords and phrases: Stochastic differential equations (SDE), Numerical solution of stochastic differential equations, Milstein method for solving SDE, Exact coupling.