Fast $$\theta $$-Maruyama scheme for stochastic Volterra integral equations of convolution type: mean-square stability and strong convergence analysis

Wang, Mengjie; Dai, Xinjie; Yan, Yu; Xiao, Aiguo

doi:10.1007/s40314-023-02248-3

Comp. Appl. Math.

2023

DOI: 10.1007/s40314-023-02248-3

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Fast $$\theta $$-Maruyama scheme for stochastic Volterra integral equations of convolution type: mean-square stability and strong convergence analysis

Mengjie Wang

Xinjie Dai

Yu Yan

et al.

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2024

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Cited by 2 publications

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Multivariate Approximation Using Symmetrized and Perturbed Hyperbolic Tangent-Activated Multidimensional Convolution-Type Operators

Anastassiou

2024

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In this article, we introduce, for the first time, multivariate symmetrized and perturbed hyperbolic tangent-activated convolution-type operators in three forms. We present their approximation properties, that is, their quantitative convergence to the unit operator via the multivariate modulus of continuity. We continue with the multivariate global smoothness preservation of these operators. We present, in detail, the related multivariate iterative approximation, as well as, multivariate simultaneous approximation, and their combinations. Using differentiability in our research, we produce higher rates of approximation, and multivariate simultaneous global smoothness preservation is also achieved.

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Multivariate Approximation Using Symmetrized and Perturbed Hyperbolic Tangent-Activated Multidimensional Convolution-Type Operators

Anastassiou

2024

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Approximation by Symmetrized and Perturbed Hyperbolic Tangent Activated Convolution-Type Operators

Anastassiou

2024

Mathematics

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In this article, for the first time, the univariate symmetrized and perturbed hyperbolic tangent activated convolution-type operators of three kinds are introduced. Their approximation properties are presented, i.e., the quantitative convergence to the unit operator via the modulus of continuity. It follows the global smoothness preservation of these operators. The related iterated approximation as well as the simultaneous approximation and their combinations, are also extensively presented. Including differentiability and fractional differentiability into our research produced higher rates of approximation. Simultaneous global smoothness preservation is also examined.

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Fast $$\theta $$-Maruyama scheme for stochastic Volterra integral equations of convolution type: mean-square stability and strong convergence analysis

Cited by 2 publications

References 46 publications

Multivariate Approximation Using Symmetrized and Perturbed Hyperbolic Tangent-Activated Multidimensional Convolution-Type Operators

Multivariate Approximation Using Symmetrized and Perturbed Hyperbolic Tangent-Activated Multidimensional Convolution-Type Operators

Approximation by Symmetrized and Perturbed Hyperbolic Tangent Activated Convolution-Type Operators

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