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The Implementation of Milstein Scheme in Two‐Dimensional SDEs Using the Fourier Method

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  • Yousef Alnafisah

Abstract

Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two‐dimensional stochastic differential equation (SDE) using Matlab program. Our numerical experiments use Matlab to show how our truncation of Itô’‐Taylor expansion at an appropriate point produces Milstein method for the SDE.

Suggested Citation

  • Yousef Alnafisah, 2018. "The Implementation of Milstein Scheme in Two‐Dimensional SDEs Using the Fourier Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnlaaa:v:2018:y:2018:i:1:n:3805042
    DOI: 10.1155/2018/3805042
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    References listed on IDEAS

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    1. P. E. Kloeden & Eckhard Platen & I. W. Wright, 1992. "The approximation of multiple stochastic integrals," Published Paper Series 1992-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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    Cited by:

    1. Albano, Giuseppina & Giorno, Virginia & Pérez-Romero, Gema & Torres-Ruiz, Francisco de Asis, 2025. "Inference on a stochastic SIR model including growth curves," Computational Statistics & Data Analysis, Elsevier, vol. 212(C).

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