Analysis and Approximation of Stochastic Multiscale Subdiffusion Driven by Fractional Gaussian Noise
Abstract
This paper investigates a stochastic multiscale subdiffusion model driven by fractional Gaussian noise, where the multiscale Abel kernel with variable exponent α(t)∈(0,1) is used to capture multiscale and crossover behavior in anomalous diffusion. The main difficulties of this model lie in the complexity of the multiscale Abel kernel (e.g. non-monotonicity and non-coercivity) and the low regularity caused by the noise. Concerning these issues, we prove the well-posedness and regularity of the mild solutions by means of solution operator approach and a perturbation technique for multiscale Abel kernel. Then both the semidiscrete-in-time and fully-discrete numerical schemes are proposed and analyzed under the low-regularity numerical analysis framework, with proved temporal and spatial convergence rates. Numerical experiments are presented to substantiate the theoretical results.
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BibTeX
@misc{dong2026analysis,
title = {{Analysis and Approximation of Stochastic Multiscale Subdiffusion Driven by Fractional Gaussian Noise}},
author = {Jincheng Dong and Ning Du and Xu Guo and Mengmeng Liu and Xiangcheng Zheng},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29533},
eprint = {2608.29533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29533},
}
RIS
TY - UNPB
TI - Analysis and Approximation of Stochastic Multiscale Subdiffusion Driven by Fractional Gaussian Noise
AU - Jincheng Dong
AU - Ning Du
AU - Xu Guo
AU - Mengmeng Liu
AU - Xiangcheng Zheng
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29533
UR - https://arxiv.org/abs/2608.29533
AB - This paper investigates a stochastic multiscale subdiffusion model driven by fractional Gaussian noise, where the multiscale Abel kernel with variable exponent α(t)∈(0,1) is used to capture multiscale and crossover behavior in anomalous diffusion. The main difficulties of this model lie in the complexity of the multiscale Abel kernel (e.g. non-monotonicity and non-coercivity) and the low regularity caused by the noise. Concerning these issues, we prove the well-posedness and regularity of the mild solutions by means of solution operator approach and a perturbation technique for multiscale Abel kernel. Then both the semidiscrete-in-time and fully-discrete numerical schemes are proposed and analyzed under the low-regularity numerical analysis framework, with proved temporal and spatial convergence rates. Numerical experiments are presented to substantiate the theoretical results.
ER -