Truncated Euler–Maruyama method for stochastic differential equations driven by fractional Brownian motion with super-linear drift coefficient

He, Jie; Gao, Shuaibin; Zhan, Weijun; Guo, Qian

doi:10.1080/00207160.2023.2266757

Cited by 1 publication

(2 citation statements)

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“…Proof. By utilizing Lemma 4, (19), and (37), the required assertion (46) is directly attained. For any 0 < * < 2, by utilizing Hölder's inequality, we obtain…”

Section: Lemmamentioning

confidence: 97%

“…Geng et al [18] studied the convergence of the truncated Euler-Maruyama method for stochastic differential equations with piecewise continuous arguments. He et al [19] studied the truncated Euler-Maruyama method for stochastic differential equations driven by fractional Brownian motion with super-linear drift coefficient. An original contribution was made in [20] by introducing the implicit split-step version of the Euler-Maruyama technique for stochastic models.…”

Section: Introductionmentioning

confidence: 99%

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Convergence Rate of the Diffused Split-Step Truncated Euler–Maruyama Method for Stochastic Pantograph Models with Lévy Leaps

Abou-Senna,

AlNemer,

Zhou

et al. 2023

Fractal Fract

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This paper studies the stochastic pantograph model, which is considered a subcategory of stochastic delay differential equations. A more general jump process, which is called the Lévy process, is added to the model for better performance and modeling situations, having sudden changes and extreme events such as market crashes in finance. By utilizing the truncation technique, we propose the diffused split-step truncated Euler–Maruyama method, which is considered as an explicit scheme, and apply it to the addressed model. By applying the Khasminskii-type condition, the convergence rate of the proposed scheme is attained in Lp(p≥2) sense where the non-jump coefficients grow super-linearly while the jump coefficient acts linearly. Also, the rate of convergence of the proposed scheme in Lp(0<p<2) sense is addressed where all the three coefficients grow beyond linearly. Finally, theoretical findings are manifested via some numerical examples.

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“…Proof. By utilizing Lemma 4, (19), and (37), the required assertion (46) is directly attained. For any 0 < * < 2, by utilizing Hölder's inequality, we obtain…”

Section: Lemmamentioning

confidence: 97%