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Weak Approximations of the Wright–Fisher Process

Author

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  • Vigirdas Mackevičius

    (Faculty of Mathematics and Informatics, Institute of Mathematics, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Gabrielė Mongirdaitė

    (Faculty of Mathematics and Informatics, Institute of Mathematics, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

Abstract

In this paper, we construct first- and second-order weak split-step approximations for the solutions of the Wright–Fisher equation. The discretization schemes use the generation of, respectively, two- and three-valued random variables at each discretization step. The accuracy of constructed approximations is illustrated by several simulation examples.

Suggested Citation

  • Vigirdas Mackevičius & Gabrielė Mongirdaitė, 2022. "Weak Approximations of the Wright–Fisher Process," Mathematics, MDPI, vol. 10(1), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:1:p:125-:d:716038
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Gytenis Lileika & Vigirdas Mackevičius, 2021. "Second-Order Weak Approximations of CKLS and CEV Processes by Discrete Random Variables," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    3. Aurélien Alfonsi, 2015. "Affine Diffusions and Related Processes: Simulation, Theory and Applications," Post-Print hal-03127212, HAL.
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    Cited by:

    1. Carmen Ionescu & Radu Constantinescu, 2022. "Solving Nonlinear Second-Order Differential Equations through the Attached Flow Method," Mathematics, MDPI, vol. 10(15), pages 1-14, August.

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