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The Semi-discrete Method for the Approximation of the Solution of Stochastic Differential Equations

In: Nonlinear Analysis, Differential Equations, and Applications

Author

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  • Ioannis S. Stamatiou

    (University of West Attica)

Abstract

We study the numerical approximation of the solution of stochastic differential equations (SDEs) that do not follow the standard smoothness assumptions. In particular, we focus on SDEs that admit solutions which take values in a certain domain; examples of these equations appear in various fields of application such as mathematical finance and natural sciences among others, where the quantity of interest may be the interest rate, which takes non-negative values, or the population dynamics which takes values between zero and one. We review the Semi-Discrete method (SD), a numerical method that has the qualitative feature of domain preservation among other desirable properties.

Suggested Citation

  • Ioannis S. Stamatiou, 2021. "The Semi-discrete Method for the Approximation of the Solution of Stochastic Differential Equations," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Nonlinear Analysis, Differential Equations, and Applications, pages 625-638, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-72563-1_23
    DOI: 10.1007/978-3-030-72563-1_23
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