Exponential Euler method for stiff SDEs driven by fractional Brownian motion

Haozhe Chen; Zhaotong Shen; Qian Yu

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arXiv · 2407.03546

Exponential Euler method for stiff SDEs driven by fractional Brownian motion

Haozhe Chen·Zhaotong Shen·Qian Yu

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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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Haozhe Chen, Zhaotong Shen, Qian Yu. 2024-07-03. Exponential Euler method for stiff SDEs driven by fractional Brownian motion. https://arxiv.org/abs/2407.03546

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