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

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2023-12-04 DOI:10.3390/fractalfract7120861

Amr Abou-Senna, Ghada AlNemer, Yongchun Zhou, Boping Tian

引用次数: 0

Abstract

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

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有列维跃迁的随机受电弓模型的扩散分步截断欧拉-Maruyama 方法的收敛率

本文研究了随机受电弓模型，该模型被认为是随机时滞微分方程的一个子类。一个更一般的跳跃过程，被称为lsamvy过程，被添加到模型中，以获得更好的性能和建模情况，具有突然变化和极端事件，如金融市场崩溃。利用截断技术，我们提出了作为显式格式的扩散分步截断Euler-Maruyama方法，并将其应用于所寻址模型。利用khasminskii型条件，得到了非跳跃系数超线性增长而跳跃系数线性增长的Lp(p≥2)意义下的收敛速度。此外，还讨论了在Lp(0

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.

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