The Experts below are selected from a list of 56031 Experts worldwide ranked by ideXlab platform
Xiaojie Wang - One of the best experts on this subject based on the ideXlab platform.
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On the backward Euler Method for a generalized Ait-Sahalia-type rate model with Poisson jumps
Numerical Algorithms, 2020Co-Authors: Yuying Zhao, Xiaojie Wang, Mengchao WangAbstract:This article aims to reveal the mean-square convergence rate of the backward Euler Method (BEM) for a generalized Ait-Sahalia interest rate model with Poisson jumps. The main difficulty in the analysis is caused by the non-globally Lipschitz drift and diffusion coefficients of the model. We show that the BEM preserves the positivity of the original problem. Furthermore, we successfully recover the mean-square convergence rate of order one-half for the BEM. The theoretical findings are accompanied by several numerical examples.
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On the backward Euler Method for a generalized Ait-Sahalia-type rate model with Poisson jumps.
arXiv: Numerical Analysis, 2020Co-Authors: Yuying Zhao, Xiaojie Wang, Mengchao WangAbstract:This article aims to reveal the mean-square convergence rate of the backward Euler Method (BEM) for a generalized Ait-Sahaliz interest rate model with Poisson jumps. The main difficulty in the analysis is caused by the non-globally Lipschitz drift and diffusion coefficients of the model. We show that the BEM preserves positivity of the original problem. Furthermore, we successfully recover the mean-square convergence rate of order one-half for the BEM. The theoretical findings are accompanied by several numerical examples.
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A transformed jump-adapted backward Euler Method for jump-extended CIR and CEV models
Numerical Algorithms, 2016Co-Authors: Xu Yang, Xiaojie WangAbstract:A novel time-stepping scheme, called transformed jump-adapted backward Euler Method, is developed in this paper to simulate a class of jump-extended CIR and CEV models. The proposed scheme is able to preserve the positivity of the underlying problems. Furthermore, its strong convergence rate of order one is recovered for the considered models with non-Lipschitz diffusion coefficients. Numerical examples are finally reported to confirm our theoretical findings.
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a note on an accelerated exponential Euler Method for parabolic spdes with additive noise
Applied Mathematics Letters, 2015Co-Authors: Xiaojie Wang, Ruisheng QiAbstract:Abstract This note aims to present further results on the accelerated exponential Euler Method proposed in Jentzen & Kloeden (2009). In contrast to very restrictive assumptions made there, we reformulate appropriate conditions on the drift coefficient of SPDEs to include a large class of nonlinear Nemytskii operators. In our setting, the Method achieves the convergence order in time of 1 2 − ϵ for arbitrarily small ϵ > 0 in the case of space–time white noise. For the trace-class noise case, multiple spatial dimensions are allowed and an optimal convergence rate is attained based on optimal regularity results of the mild solution, which improves the corresponding convergence results in Jentzen et al. (2011).
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a note on an accelerated exponential Euler Method for parabolic spdes with additive noise
Applied Mathematics Letters, 2015Co-Authors: Xiaojie WangAbstract:Abstract This note aims to present further results on the accelerated exponential Euler Method proposed in Jentzen & Kloeden (2009). In contrast to very restrictive assumptions made there, we reformulate appropriate conditions on the drift coefficient of SPDEs to include a large class of nonlinear Nemytskii operators. In our setting, the Method achieves the convergence order in time of 1 2 − ϵ for arbitrarily small ϵ > 0 in the case of space–time white noise. For the trace-class noise case, multiple spatial dimensions are allowed and an optimal convergence rate is attained based on optimal regularity results of the mild solution, which improves the corresponding convergence results in Jentzen et al. (2011).
Alexander Aleksandrov - One of the best experts on this subject based on the ideXlab platform.
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Proofs for "Discretization of Homogeneous Systems Using Euler Method with a State-Dependent Step
2019Co-Authors: Denis Efimov, Andrey Polyakov, Alexander AleksandrovAbstract:This note contains some proofs for the paper "Discretization of Homogeneous Systems Using Euler Method with a State-Dependent Step" of the same authors.
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Discretization of Homogeneous Systems Using Euler Method with a State-Dependent Step
Automatica, 2019Co-Authors: Denis Efimov, Andrey Polyakov, Alexander AleksandrovAbstract:Numeric approximations to the solutions of asymptotically stable homogeneous systems by Euler Method, with a step of discretization scaled by the state norm, are investigated (for the explicit and implicit integration schemes). It is proven that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time depending on the degree of homogeneity of the system, but in an infinite number of discretization iterations. The maximal admissible step can be estimated by analyzing the system properties on the sphere. It is shown that the absolute and relative errors of the discretizations are globally bounded functions, thus the approximations approaching the solutions with the step converging to zero. In addition, it is established that the proposed discretization approach preserves robustness with respect to exogenous perturbations. Efficiency of the designed discretization algorithms is demonstrated in simulations.
Chiping Zhang - One of the best experts on this subject based on the ideXlab platform.
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The Convergence and MS Stability of Exponential Euler Method for Semilinear Stochastic Differential Equations
Abstract and Applied Analysis, 2012Co-Authors: Chunmei Shi, Yu Xiao, Chiping ZhangAbstract:The numerical approximation of exponential Euler Method is constructed for semilinear stochastic differential equations (SDEs). The convergence and mean-square (MS) stability of exponential Euler Method are investigated. It is proved that the exponential Euler Method is convergent with the strong order 1/2 for semilinear SDEs. A mean-square linear stability analysis shows that the stability region of exponential Euler Method contains that of EM Method and stochastic Theta Method (0≤
Mengchao Wang - One of the best experts on this subject based on the ideXlab platform.
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On the backward Euler Method for a generalized Ait-Sahalia-type rate model with Poisson jumps
Numerical Algorithms, 2020Co-Authors: Yuying Zhao, Xiaojie Wang, Mengchao WangAbstract:This article aims to reveal the mean-square convergence rate of the backward Euler Method (BEM) for a generalized Ait-Sahalia interest rate model with Poisson jumps. The main difficulty in the analysis is caused by the non-globally Lipschitz drift and diffusion coefficients of the model. We show that the BEM preserves the positivity of the original problem. Furthermore, we successfully recover the mean-square convergence rate of order one-half for the BEM. The theoretical findings are accompanied by several numerical examples.
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On the backward Euler Method for a generalized Ait-Sahalia-type rate model with Poisson jumps.
arXiv: Numerical Analysis, 2020Co-Authors: Yuying Zhao, Xiaojie Wang, Mengchao WangAbstract:This article aims to reveal the mean-square convergence rate of the backward Euler Method (BEM) for a generalized Ait-Sahaliz interest rate model with Poisson jumps. The main difficulty in the analysis is caused by the non-globally Lipschitz drift and diffusion coefficients of the model. We show that the BEM preserves positivity of the original problem. Furthermore, we successfully recover the mean-square convergence rate of order one-half for the BEM. The theoretical findings are accompanied by several numerical examples.
Denis Efimov - One of the best experts on this subject based on the ideXlab platform.
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Proofs for "Discretization of Homogeneous Systems Using Euler Method with a State-Dependent Step
2019Co-Authors: Denis Efimov, Andrey Polyakov, Alexander AleksandrovAbstract:This note contains some proofs for the paper "Discretization of Homogeneous Systems Using Euler Method with a State-Dependent Step" of the same authors.
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Discretization of Homogeneous Systems Using Euler Method with a State-Dependent Step
Automatica, 2019Co-Authors: Denis Efimov, Andrey Polyakov, Alexander AleksandrovAbstract:Numeric approximations to the solutions of asymptotically stable homogeneous systems by Euler Method, with a step of discretization scaled by the state norm, are investigated (for the explicit and implicit integration schemes). It is proven that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time depending on the degree of homogeneity of the system, but in an infinite number of discretization iterations. The maximal admissible step can be estimated by analyzing the system properties on the sphere. It is shown that the absolute and relative errors of the discretizations are globally bounded functions, thus the approximations approaching the solutions with the step converging to zero. In addition, it is established that the proposed discretization approach preserves robustness with respect to exogenous perturbations. Efficiency of the designed discretization algorithms is demonstrated in simulations.