What is it about?
We first loosen the assumption of the global Lipschitz condition to the local Lipschitz condition and proceed to prove the well—posedness, and then we study the strong convergence order of the numerical method.
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Why is it important?
We investigate the strong convergence order with the local Lipschitz condition, which is inherently lower than the strong convergence order O/2 with the global Lipschitz condition.
Perspectives
We only show that the strong convergence order with the local Lipschitz condition, which is inherently lower than the strong convergence order O/2 with the global Lipschitz condition. To prove the convergence rate under non—Lipschitz condition is still an open problem.
Zhaoqiang Yang
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This page is a summary of: Strong Convergence of a Modified Euler—Maruyama Method for Mixed Stochastic Fractional Integro—Differential Equations with Local Lipschitz Coefficients, Fractal and Fractional, May 2025, MDPI AG,
DOI: 10.3390/fractalfract9050296.
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