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

Bahar Akhtari () and Panyu Wu ()
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Bahar Akhtari: University of Isfahan
Panyu Wu: Shandong University

Journal of Theoretical Probability, 2025, vol. 38, issue 4, 1-21

Abstract: 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.

Keywords: Milstein scheme; Stochastic differential equations; G-Brownian motion; G-Itô’s formula; 60H10; 60H35; 65C30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01441-w

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