The Experts below are selected from a list of 23199 Experts worldwide ranked by ideXlab platform
Tianxiao Wang - One of the best experts on this subject based on the ideXlab platform.
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mean field linear quadratic gaussian lqg games for Stochastic Integral systems
IEEE Transactions on Automatic Control, 2016Co-Authors: Jianhui Huang, Tianxiao WangAbstract:In this technical note, we formulate and investigate a class of mean-field linear-quadratic-Gaussian (LQG) games for Stochastic Integral systems. Unlike other literature on mean-field games where the individual states follow the controlled Stochastic differential equations (SDEs), the individual states in our large-population system are characterized by a class of Stochastic Volterra-type Integral equations. We obtain the Nash certainty equivalence (NCE) equation and hence derive the set of associated decentralized strategies. The $\epsilon$ -Nash equilibrium properties are also verified. Due to the intrinsic Integral structure, the techniques and estimates applied here are significantly different from those existing results in mean-field LQG games for Stochastic differential systems. For example, some Fredholm equation in the mean-field setup is introduced for the first time. As for applications, two types of Stochastic delayed systems are formulated as the special cases of our Stochastic Integral system, and relevant mean-field LQG games are discussed.
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Optimal Control Problems of Forward-Backward Stochastic Volterra Integral Equations
arXiv: Optimization and Control, 2014Co-Authors: Yufeng Shi, Tianxiao Wang, Jiongmin YongAbstract:Optimal control problems of forward-backward Stochastic Volterra Integral equations (FBSVIEs in short) are formulated and studied. A general duality principle is established for linear backward Stochastic Integral equation and linear Stochastic Fredholm-Volterra Integral equation with mean-field. With the help of such a duality principle, together with some other new delicate and subtle skills, Pontryagin type maximum principles are proved for two optimal control problems of FBSVIEs.
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mean field linear quadratic gaussian lqg games for Stochastic Integral systems
arXiv: Probability, 2013Co-Authors: Jianhui Huang, Tianxiao WangAbstract:In this paper we discuss a class of mean field linear-quadratic-Gaussian (LQG) games for large population system which has never been addressed by existing literature. The features of our works are sketched as follows. First of all, our state is modeled by Stochastic Volterra-type equation which leads to some new study on Stochastic "Integral" system. This feature makes our setup significantly different from the previous mean field games where the states always follow some Stochastic "differential" equations. Actually, our Stochastic Integral system is rather general and can be viewed as natural generalization of Stochastic differential equations. In addition, it also includes some types of Stochastic delayed systems as its special cases. Second, some new techniques are explored to tackle our mean-field LQG games due to the special structure of Integral system. For example, unlike the Riccati equation in linear controlled differential system, some Fredholm-type equations are introduced to characterize the consistency condition of our Integral system via the resolvent kernels. Third, based on the state aggregation technique, the Nash certainty equivalence (NCE) equation is derived and the set of associated decentralized controls are verified to satisfy the $\epsilon$-Nash equilibrium property. To this end, some new estimates of Stochastic Volterra equations are developed which also have their own interests.
Jianhui Huang - One of the best experts on this subject based on the ideXlab platform.
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mean field linear quadratic gaussian lqg games for Stochastic Integral systems
IEEE Transactions on Automatic Control, 2016Co-Authors: Jianhui Huang, Tianxiao WangAbstract:In this technical note, we formulate and investigate a class of mean-field linear-quadratic-Gaussian (LQG) games for Stochastic Integral systems. Unlike other literature on mean-field games where the individual states follow the controlled Stochastic differential equations (SDEs), the individual states in our large-population system are characterized by a class of Stochastic Volterra-type Integral equations. We obtain the Nash certainty equivalence (NCE) equation and hence derive the set of associated decentralized strategies. The $\epsilon$ -Nash equilibrium properties are also verified. Due to the intrinsic Integral structure, the techniques and estimates applied here are significantly different from those existing results in mean-field LQG games for Stochastic differential systems. For example, some Fredholm equation in the mean-field setup is introduced for the first time. As for applications, two types of Stochastic delayed systems are formulated as the special cases of our Stochastic Integral system, and relevant mean-field LQG games are discussed.
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mean field linear quadratic gaussian lqg games for Stochastic Integral systems
arXiv: Probability, 2013Co-Authors: Jianhui Huang, Tianxiao WangAbstract:In this paper we discuss a class of mean field linear-quadratic-Gaussian (LQG) games for large population system which has never been addressed by existing literature. The features of our works are sketched as follows. First of all, our state is modeled by Stochastic Volterra-type equation which leads to some new study on Stochastic "Integral" system. This feature makes our setup significantly different from the previous mean field games where the states always follow some Stochastic "differential" equations. Actually, our Stochastic Integral system is rather general and can be viewed as natural generalization of Stochastic differential equations. In addition, it also includes some types of Stochastic delayed systems as its special cases. Second, some new techniques are explored to tackle our mean-field LQG games due to the special structure of Integral system. For example, unlike the Riccati equation in linear controlled differential system, some Fredholm-type equations are introduced to characterize the consistency condition of our Integral system via the resolvent kernels. Third, based on the state aggregation technique, the Nash certainty equivalence (NCE) equation is derived and the set of associated decentralized controls are verified to satisfy the $\epsilon$-Nash equilibrium property. To this end, some new estimates of Stochastic Volterra equations are developed which also have their own interests.
Farshid Mirzaee - One of the best experts on this subject based on the ideXlab platform.
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cubic b spline approximation for linear Stochastic integro differential equation of fractional order
Journal of Computational and Applied Mathematics, 2020Co-Authors: Farshid Mirzaee, Sahar AlipourAbstract:Abstract In this paper, the cubic B-spline collocation method is used for solving the Stochastic integro-differential equation of fractional order. we show that Stochastic integro-differential equation of fractional order is equivalent to a modified Stochastic Integral equation. Then we apply the proposed method to obtain a numerical scheme of the modified Stochastic Integral equation. Using this method, the problem solving turns into a linear system solution of equations. Also, the convergence analysis of this numerical approach has been discussed. In the end, examples are given to test the accuracy and the implementation of the method. The results are compared with the results obtained by other methods to verify that this method is accurate and efficient.
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numerical solution of two dimensional weakly singular Stochastic Integral equations on non rectangular domains via radial basis functions
Engineering Analysis With Boundary Elements, 2019Co-Authors: Nasrin Samadyar, Farshid MirzaeeAbstract:Abstract In this paper, a meshfree method based on radial basis functions (RBFs) is applied to solve two-dimensional weakly singular Stochastic Integral equations on non-rectangular domains. RBFs interpolation together quadrature rule is used to transform the solution of mentioned problem to the linear system of algebraic equations which can be solved by using direct method or iterative method. The most important advantage of this scheme is that it is independent of the geometry of the region and so it can be applied for solving different kinds of Integral equations on irregular domains. Convergence analysis and error estimate of the proposed method have been investigated. In order to show accuracy and efficiency of the proposed approach, it is applied to solve two examples and maximum error and the root mean squared error (RMS-error) are reported. The obtained results reveal that the suggested method is very accurate and efficient.
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Using radial basis functions to solve two dimensional linear Stochastic Integral equations on non-rectangular domains
Engineering Analysis with Boundary Elements, 2018Co-Authors: Farshid Mirzaee, Nasrin SamadyarAbstract:Abstract The main goal of this paper is presenting an efficient numerical scheme to solve two dimensional linear Stochastic Integral equations on non-rectangular domains. The proposed method is based on combination of radial basis functions (RBFs) interpolation and Gauss–Legendre quadrature rule for double Integrals. The most important advantage of proposed method is that it does not require any discretization and so it is independent of the geometry of the domains. Thus, many problems on the irregular domains can be solved. By using this method, the solution of consideration problem is converted to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. Also, the convergence analysis of this approach is discussed. Finally, applicability of the present method is investigated through illustrative examples.
Nasrin Samadyar - One of the best experts on this subject based on the ideXlab platform.
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numerical solution of two dimensional weakly singular Stochastic Integral equations on non rectangular domains via radial basis functions
Engineering Analysis With Boundary Elements, 2019Co-Authors: Nasrin Samadyar, Farshid MirzaeeAbstract:Abstract In this paper, a meshfree method based on radial basis functions (RBFs) is applied to solve two-dimensional weakly singular Stochastic Integral equations on non-rectangular domains. RBFs interpolation together quadrature rule is used to transform the solution of mentioned problem to the linear system of algebraic equations which can be solved by using direct method or iterative method. The most important advantage of this scheme is that it is independent of the geometry of the region and so it can be applied for solving different kinds of Integral equations on irregular domains. Convergence analysis and error estimate of the proposed method have been investigated. In order to show accuracy and efficiency of the proposed approach, it is applied to solve two examples and maximum error and the root mean squared error (RMS-error) are reported. The obtained results reveal that the suggested method is very accurate and efficient.
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Using radial basis functions to solve two dimensional linear Stochastic Integral equations on non-rectangular domains
Engineering Analysis with Boundary Elements, 2018Co-Authors: Farshid Mirzaee, Nasrin SamadyarAbstract:Abstract The main goal of this paper is presenting an efficient numerical scheme to solve two dimensional linear Stochastic Integral equations on non-rectangular domains. The proposed method is based on combination of radial basis functions (RBFs) interpolation and Gauss–Legendre quadrature rule for double Integrals. The most important advantage of proposed method is that it does not require any discretization and so it is independent of the geometry of the domains. Thus, many problems on the irregular domains can be solved. By using this method, the solution of consideration problem is converted to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. Also, the convergence analysis of this approach is discussed. Finally, applicability of the present method is investigated through illustrative examples.
Vladas Pipiras - One of the best experts on this subject based on the ideXlab platform.
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on Integral representations of operator fractional brownian fields
Statistics & Probability Letters, 2014Co-Authors: Changryong Baek, Gustavo Didier, Vladas PipirasAbstract:Abstract Operator fractional Brownian fields (OFBFs) are Gaussian, stationary-increment vector random fields that satisfy the operator self-similarity relation { X ( c E t ) } t ∈ R m = L { c H X ( t ) } t ∈ R m . We establish a general harmonizable representation (Fourier domain Stochastic Integral) for OFBFs. Under additional assumptions, we also show how the harmonizable representation can be re-expressed as a moving average Stochastic Integral, thus answering an open problem described in Bierme et al. (2007).
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on Integral representations of operator fractional brownian fields
arXiv: Probability, 2014Co-Authors: Changryong Baek, Gustavo Didier, Vladas PipirasAbstract:Operator fractional Brownian fields (OFBFs) are Gaussian, stationary-increment vector random fields that satisfy the operator self-similarity relation {X(c^{E}t)}_{t in R^m} L= {c^{H}X(t)}_{t in R^m}. We establish a general harmonizable representation (Fourier domain Stochastic Integral) for OFBFs. Under additional assumptions, we also show how the harmonizable representation can be reexpressed as a moving average Stochastic Integral, thus answering an open problem described in Bierme et al.(2007), "Operator scaling stable random fields", Stochastic Processes and their Applications 117, 312--332.
