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Milstein Scheme for Stochastic Differential Equations Driven by G-Brownian Motion

Author

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  • Bahar Akhtari

    (University of Isfahan
    School of Mathematics, Institute for Research in Fundamental Sciences (IPM))

  • Panyu Wu

    (Shandong University)

Abstract

Driven by the emergence of stochastic differential equations stochastic differential equations (SDEs) influenced by G-Brownian motion in the context of uncertain data across various financial scenarios, there is a pressing need to develop efficient numerical schemes for approximating these types of SDEs. Recently, several discretization schemes have been introduced to numerically solve G-SDEs using the standard Euler–Maruyama method. This study presents a first-order discretization scheme based on the G-Itô’s formula for G-SDEs. Furthermore, we examine the convergence of the proposed scheme and explore its asymptotic behavior in the $$L^2$$ L 2 sense. The findings confirm that the numerical method exhibits stability against small perturbations.

Suggested Citation

  • Bahar Akhtari & Panyu Wu, 2025. "Milstein Scheme for Stochastic Differential Equations Driven by G-Brownian Motion," Journal of Theoretical Probability, Springer, vol. 38(4), pages 1-21, December.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:4:d:10.1007_s10959-025-01441-w
    DOI: 10.1007/s10959-025-01441-w
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