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Milstein scheme for a stochastic semilinear subdiffusion equation driven by fractionally integrated multiplicative noise
Wu, Xiaolei Yan, Yubin
Wu, Xiaolei
Yan, Yubin
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2025-05-14
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Abstract
This paper investigates the strong convergence of a Milstein scheme for a stochastic semilinear subdiffusion equation driven by fractionally integrated multiplicative noise. The existence and uniqueness of the mild solution are established via the Banach fixed point theorem. Temporal and spatial regularity properties of the mild solution are derived using the semigroup approach. For spatial discretization, the standard Galerkin finite element method is employed, while the Grünwald–Letnikov method is used for time discretization. The Milstein scheme is utilized to approximate the multiplicative noise. For sufficiently smooth noise, the proposed scheme achieves the temporal strong convergence order of O(τα), α∈(0,1). Numerical experiments are presented to verify that the computational results are consistent with the theoretical predictions.
Citation
Wu, X., & Yan, Y. (2025). Milstein scheme for a stochastic semilinear subdiffusion equation driven by fractionally integrated multiplicative noise. Fractal and Fractional, 9(5), article-number 314. https://doi.org/10.3390/fractalfract9050314
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MDPI
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Fractal and Fractional
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10.3390/fractalfract9050314
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Article
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en
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© 2025 by the authors. Licensee MDPI, Basel, Switzerland.
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2504-3110
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This research was funded by the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province (Grant No. 20240037), the Research Project Supported by Shanxi Scholarship Council of China (Grant No. 2024-139), the Lvliang High Tech Research and Development Program (Grant No. 2023GXYF14), and the Shanxi Provincial Art Science Planning Project (Grant No. 24BA106).