Exponential Euler method for stiff SDEs driven by fractional Brownian motion

2024/07/03 by Haozhe Chen, Chen, Haozhe, Zhaotong Shen +3
Engineering · #FOS: Mathematics #Fluid Dynamics and Thin Films #Fluid Dynamics and Turbulent Flows #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2407.03546

openalex publication_date 2024/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a recent paper by Kamrani et al. (2024), exponential Euler method for stiff stochastic differential equations with additive fractional Brownian noise was discussed, and the convergence order close to the Hurst parameter H was proved. Utilizing the technique of Malliavin derivative, we prove the exponential Euler scheme and obtain a convergence order of one, which is the optimal rate in numerical simulation.

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