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Journal of Computational Mathematics 2024年第4期42卷 1109-1123页

作者： Guangqiang Lan Yu Jiang College of Mathematics and Physics Beijing University of Chemical TechnologyBeijing 100029China

Convergence of modified truncated Euler-Maruyama(MTEM)method for stochastic differential equations(SDEs)with(1/2+α)-Holder continuous diffusion coefficients are investigated in this *** prove that the MTEM method for... 详细信息

关键词： stochastic differential equations Modified truncated Euler-Maruyama method Strong convergence One-sided Lipschitz Holder continuous

stochastic differential equations Driven by Multi-fractional Brownian Motion and Poisson Point Process

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Journal of Partial differential equations 2019年第4期32卷 352-368页

作者： LIU Hailing XU Liping LI Zhi School of Information and Mathematics Yangtze UniversityJingzhou 434023China

In this paper,we study a class of stochastic differential equations with additive noise that contains a non-stationary multifractional Brownian motion(mBm)with a Hurst parameter as a function of time and a Poisson point process of class(QL).The differential equation of this kind is motivated by the reserve processes in a general insurance model,in which between the claim payment and the past history of liability present the long term *** using the variable order fractional calculus on the fractional Wiener-Poisson space and a multifractional derivative operator,and employing Girsanov theorem for multifractional Brownian motion,we prove the existence of weak solutions to the SDEs under consideration,As a consequence,we deduce the uniqueness in law and the pathwise uniqueness.

关键词： stochastic differential equations multifractional Brownian motion fractional Wiener-Poisson space Poisson point process Girsanov theorem

Some Properties of stochastic differential equations Driven by the G-Brownian Motion

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Acta Mathematica Sinica,English Series 2013年第5期29卷 923-942页

作者： Qian LIN Institute for Financial Studies Shandong University

In this paper, we study the property of continuous dependence on the parameters of stochastic integrals and solutions of stochastic differential equations driven by the G-Brownian motion. In addition, the uniqueness a... 详细信息

关键词： G-expectation continuous paths G-Brownian motion stochastic differential equations

THE CONVERGENCE OF TRUNCATED EULER-MARUYAMA METHOD FOR stochastic differential equations WITH PIECEWISE CONTINUOUS ARGUMENTS UNDER GENERALIZED ONE-SIDED LIPSCHITZ CONDITION

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Journal of Computational Mathematics 2023年第4期41卷 663-682页

作者： Yidan Geng Minghui Song Mingzhu Liu School of Mathematics Harbin Institute of TechnologyHarbin 150001China Digital Technology Research Center China Electronics Standardization InstituteBeijing100007China

In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth *** the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not *** overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical *** is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional *** example is presented to illustrate the analytical theory.

关键词： stochastic differential equations Piecewise continuous argument One-sided Lipschitz condition Truncated Euler-Maruyama method

Data-Driven Discovery of stochastic differential equations

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Engineering 2022年第10期17卷 244-252页

作者： Yasen Wang Huazhen Fang Junyang Jin Guijun Ma Xin He Xing Dai Zuogong Yue Cheng Cheng Hai-Tao Zhang Donglin Pu Dongrui Wu Ye Yuan Jorge Gonçalves Jürgen Kurths Han Ding School of Mechanical Science and Engineering Huazhong University of Science and TechnologyWuhan 430074China State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and TechnologyWuhan 430074China Department of Mechanical Engineering University of KansasLawrenceKS 66045USA HUST-Wuxi Research Institute Wuxi 214174China Key Laboratory of Image Processing and Intelligent Control School of Artificial Intelligence and AutomationHuazhong University of Science and TechnologyWuhan 430074China Department of Plant Sciences University of CambridgeCambridge CB23EAUK Luxembourg Centre for Systems Biomedicine University of LuxembourgBelvaux 4367Luxembourg Department of Physics Humboldt University of BerlinBerlin 12489Germany Department of Complexity Science Potsdam Institute for Climate Impact ResearchPotsdam 14473Germany

stochastic differential equations(SDEs)are mathematical models that are widely used to describe complex processes or phenomena perturbed by random noise from different *** identification of SDEs governing a system is often a challenge because of the inherent strong stochasticity of data and the complexity of the system’s *** practical utility of existing parametric approaches for identifying SDEs is usually limited by insufficient data *** study presents a novel framework for identifying SDEs by leveraging the sparse Bayesian learning(SBL)technique to search for a parsimonious,yet physically necessary representation from the space of candidate basis *** importantly,we use the analytical tractability of SBL to develop an efficient way to formulate the linear regression problem for the discovery of SDEs that requires considerably less time-series *** effectiveness of the proposed framework is demonstrated using real data on stock and oil prices,bearing variation,and wind speed,as well as simulated data on well-known stochastic dynamical systems,including the generalized Wiener process and Langevin *** framework aims to assist specialists in extracting stochastic mathematical models from random phenomena in the natural sciences,economics,and engineering fields for analysis,prediction,and decision making.

关键词： Data-driven method System identification Sparse Bayesian learning stochastic differential equations Random phenomena

PI-VEGAN:Physics Informed Variational Embedding Generative Adversarial Networks for stochastic differential equations

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Numerical Mathematics(Theory,Methods and Applications) 2023年第4期16卷 931-953页

作者： Ruisong Gao Yufeng Wang Min Yang Chuanjun Chen School of Mathematics and Information Sciences Yantai UniversityYantaiChina

We present a new category of physics-informed neural networks called physics informed variational embedding generative adversarial network(PI-VEGAN),that effectively tackles the forward,inverse,and mixed problems of stochastic differential *** these scenarios,the governing equations are known,but only a limited number of sensor measurements of the system parameters are *** integrate the governing physical laws into PI-VEGAN with automatic differentiation,while introducing a variational encoder for approximating the latent variables of the actual distribution of the *** latent variables are integrated into the generator to facilitate accurate learning of the characteristics of the stochastic partial *** model consists of three components,namely the encoder,generator,and discriminator,each of which is updated alternatively employing the stochastic gradient descent *** evaluate the effectiveness of PI-VEGAN in addressing forward,inverse,and mixed problems that require the concurrent calculation of system parameters and *** results demonstrate that the proposed method achieves satisfactory stability and accuracy in comparison with the previous physics-informed generative adversarial network(PI-WGAN).

关键词： stochastic differential equations physics-informed variational inference generative adversarial networks inverse problems

Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations

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Science China Mathematics 2017年第4期60卷 735-744页

作者： YUE Chao School of Economics and Trade Zhengzhou University of Aeronautics Zhengzhou 450015 China

We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When 0 ≥ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h 〉 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.

关键词： stochastic differential equations mean-square stability improved split-step theta methods expo-nential mean-square stability

CONVERGENCE ANALYSIS OF PARAREAL ALGORITHM BASED ON MILSTEIN SCHEME FOR stochastic differential equations

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Journal of Computational Mathematics 2020年第3期38卷 487-501页

作者： Liying Zhang Jing Wang Weien Zhou Landong Liu Li Zhang School of Mathematical Science China University of Mining and TechnologyBeijing 100083China National Innovation Institute of Defense Technology Chinese Academy of Military ScienceBeijing 100101China Department of Foundation Courses Beijing Union UniversityBeijing 100101China

In this paper,we propose a parareal algorithm for stochastic differential equations(SDEs),which proceeds as a two-level temporal parallelizable integrator with the Milstein scheme as the coarse propagator and the exact solution as the fine *** convergence order of the proposed algorithm is analyzed under some regular ***,numerical experiments are dedicated to illustrate the convergence and the convergence order with respect to the iteration number k,which show the efficiency of the proposed method.

关键词： stochastic differential equations Parareal algorithm Convergence stochastic Taylor expansion Milstein scheme

The Link between stochastic differential equations with Non-Markovian Coefficients and Backward stochastic Partial differential equations

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Acta Mathematica Sinica,English Series 2021年第3期37卷 447-457页

作者： Lin LIN Fang XU Qi ZHANG School of Arts and Sciences Shanghai Dianji UniversityShanghai 201306P.R.China School of Mathematical Sciences Fudan UniversityShanghai 200433P.R.China

In this paper, we conjecture and prove the link between stochastic differential equations with non-Markovian coefficients and nonlinear parabolic backward stochastic partial differential equations, which is an extension of such kind of link in Markovian framework to non-Markovian *** from Markovian framework, where the corresponding partial differential equation is deterministic, the backward stochastic partial differential equation here has a pair of adapted solutions, and thus the link has a much different form. Moreover, two examples are given to demonstrate the applications of the derived link.

关键词： Backward stochastic partial differential equations stochastic differential equations nonMarkovian coefficients Girsanov transformation Feynman–Kac formula

The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional stochastic differential equations

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Advances in Applied Mathematics and Mechanics 2023年第4期15卷 852-879页

作者： Shanshan Xu Lin Wang Wenqiang Wang School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanHunan 411105China

In this paper,we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations(VFSDEs).We futher constructe the Euler-Maruyama method to solve the equations and prove the convergence in mean and the strong convergence of the *** particular,when the fractional order is no longer varying,the conclusions obtained are consistent with the relevant conclusions in the existing ***,the numerical experiments at the end of the article verify the correctness of the theoretical results obtained.

关键词： Variable-order Caputo fractional derivative stochastic differential equations Euler-Maruyama method convergence multiplicative noise