JISE


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Journal of Information Science and Engineering, Vol. 36 No. 6, pp. 1223-1232


Comparison Between Milstein and Exact Coupling Methods using MATLAB for a Particular Two-Dimensional Stochastic Differential Equation


YOUSEF ALI ALNAFISAH
Mathematics Department
Qassim University
P. O. Box 6644, Buraydah 51452, Saudi Arabia
E-mail: UAN 0261@hotmail.com


We compare Milstein and exact coupling methods for the strong approximation of solutions to stochastic differential equations (SDE), which are driven by Brownian motion. Both of these methods attain an order one convergence under the nondegeneracy assumption of the diffusion term for the exact coupling method. We also compare their implementation using MATLAB. A particular two-dimensional SDE is used in the implementation for comparing their results. Moreover, the performance of both methods and the amount of time required to obtain the result are also analyzed. It is interesting to mention that this comparison is very important in several areas, such as stochastic analysis, financial mathematics and some physical applications.


Keywords: Stochastic differential equations (SDE), numerical solution of stochastic differential equations, Milstein method for solving DSE, exact coupling, coupling

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