STRONG CONVERGENCE OF LEVY-DRIVEN MIXED STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH APPLICATION TO THE ROUGH MIXED VOLATILITY MODELS

doi:10.3934/cac.2025005

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	STRONG CONVERGENCE OF LEVY-DRIVEN MIXED STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH APPLICATION TO THE ROUGH MIXED VOLATILITY MODELS
	Yang, Zhaoqiang1,2 ; Xu, Chenglong 1
	2025-06
发表期刊	COMMUNICATIONS ON ANALYSIS AND COMPUTATION
卷号	4 页码:1-38
摘要	In this paper, we focus on investigating the strong convergence of Levy-driven mixed stochastic integro-differential equations (L-mSIDEs) with singular kernels under the local Lipschitz and linear growth conditions. First, we transform the L-mSIDEs into an equivalent Levy-driven mixed stochastic Volterra integral equations (L-mSVIEs) by a fractional calculus technique. Then, we rigorously analyze the existence, uniqueness, boundedness, and the continuous dependence of the analytical solutions to the L-mSVIEs. After that, we propose a modified stochastic Milstein method as a numerical solution for the L-mSVIEs by the local truncation technique and sum-of-exponentials (SOE) approximation scheme to improve the calculations effectively. Specifically, we derive the precise convergence order of this method under the same condition in the L2 sense. Our stochastic Milstein-scheme can achieve the desired accuracy O(epsilon), and the computational cost of a single sample from O(N2 + epsilon-2- 2 ) and O(N + epsilon-1- 1 ) to O(N log N + epsilon- 2 ) and O (log N + epsilon-1- 1 ) when T >> 1, and for T approximate to 1, the reductions are to O(N log2 N+epsilon- 2 ) and O(log2 N + epsilon-1-1 ), respectively. To verify the accuracy and robustness of our theoretical framework, we conduct numerical experiments using rough mixed volatility models. By comparing our results with [18], we demonstrate that the current approach not only circumvents the restrictive integrability conditions imposed by singular kernels, but also achieves a rigorous convergence order in the L2-norm framework.
关键词	Levy-driven mixed stochastic integro-differential equations fractional calculus mixed stochastic Volterra integral equation stochastic Milstein-scheme convergence order rough mixed volatility models
DOI	10.3934/cac.2025005
收录类别	ESCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:001479020600001
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
原始文献类型	Article
EISSN	2837-0562
文献类型	期刊论文
条目标识符	http://ir.lzufe.edu.cn/handle/39EH0E1M/39148
专题	图书馆
通讯作者	Xu, Chenglong
作者单位	1.Shanghai Univ Finance & Econ, Sch Math, Shanghai 200433, Peoples R China; 2.Lanzhou Univ Finance & Econ, Lib & Sch Stat, Lanzhou 730101, Gansu, Peoples R China
第一作者单位	兰州财经大学
推荐引用方式 GB/T 7714	Yang, Zhaoqiang,Xu, Chenglong. STRONG CONVERGENCE OF LEVY-DRIVEN MIXED STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH APPLICATION TO THE ROUGH MIXED VOLATILITY MODELS[J]. COMMUNICATIONS ON ANALYSIS AND COMPUTATION,2025,4:1-38.
APA	Yang, Zhaoqiang,&Xu, Chenglong.(2025).STRONG CONVERGENCE OF LEVY-DRIVEN MIXED STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH APPLICATION TO THE ROUGH MIXED VOLATILITY MODELS.COMMUNICATIONS ON ANALYSIS AND COMPUTATION,4,1-38.
MLA	Yang, Zhaoqiang,et al."STRONG CONVERGENCE OF LEVY-DRIVEN MIXED STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH APPLICATION TO THE ROUGH MIXED VOLATILITY MODELS".COMMUNICATIONS ON ANALYSIS AND COMPUTATION 4(2025):1-38.