Convergence of Modified Truncated Euler-Maruyama Method for Stochastic Differential Equations with Hölder Diffusion Coefficients (Journal of Computational Mathematics, 2024)
Convergence of modified truncated Euler-Maruyama (MTEM) method for stochasticdifferential equations (SDEs) with $(1/2 + α)$-Hölder continuous diffusion coefficients areinvestigated in this paper. We prove that the MTEM method for SDE converges to theexact solution in $L^q$ sense under given conditions. Two examples are provided to supportour conclusions.
Keywords: Stochastic differential equations; Modified truncated Euler-Maruyama method; Strong convergence; One-sided Lipschitz; Hölder continuous.