Convergence of discrete approximation for differential linear stochastic complementarity systems

In this paper, we investigate a class of differential linear stochastic complementarity system consisting of an ordinary differential equation and a stochastic complementarity problem. The existence of solutions for such system is obtained under two cases of the coefficient matrix of the linear stoc...

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Vydáno v:Numerical algorithms Ročník 87; číslo 1; s. 223 - 262
Hlavní autoři: Luo, Jianfeng, Wang, Xiaozhou, Zhao, Yi
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.05.2021
Springer Nature B.V
Témata:
Algebra
Algorithms
Approximation
Computer Science
Convergence
Differential equations
Expected values
Mathematical functions
Matrices (mathematics)
Numeric Computing
Numerical Analysis
Ordinary differential equations
Original Paper
Random variables
Regularization
Theory of Computation
Epiconvergence almost surely
Progressive hedging method
Random lower semi-continuous
Carathéodory weak solution
ISSN:1017-1398, 1572-9265
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Shrnutí:In this paper, we investigate a class of differential linear stochastic complementarity system consisting of an ordinary differential equation and a stochastic complementarity problem. The existence of solutions for such system is obtained under two cases of the coefficient matrix of the linear stochastic complementarity problem: P-matrix and positive semi-definite matrix. As for the first case, the sample average approximate method and time-stepping method are adopted to get the numerical solutions. Furthermore, a regularization approximation is introduced to the second case to ensure the uniqueness of solutions. The corresponding convergence analysis is conducted, and numerical examples are presented to illustrate the convergence results we derived. Finally, we provide numerical results which come from applications involving dynamic traffic flow problems to support our theorems.
Bibliografie:ObjectType-Article-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-00965-y