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Averaging principle for stochastic fractional differential equations driven by Tempered Fractional Brownian Motion with two-time-scale Markov switching

Author

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  • Zhao, Hengzhi
  • Wu, Qin
  • Zhang, Jiwei
  • Lu, Jing
  • Lv, Dongsheng

Abstract

This paper investigates the dynamics of stochastic fractional differential equations driven by Tempered Fractional Brownian Motion (TFBM) under the influence of two-time-scale Markov switching. We successfully overcame the challenges posed by the singularity issues in stochastic integrals driven by TFBM, establishing boundedness and continuity estimates for the system. Under the assumption of Lipschitz conditions, we further developed an averaging principle, providing new mathematical tools for the theoretical analysis and numerical simulation of complex dynamic systems. These theoretical advancements significantly simplify the analysis of complex systems, enhancing both the feasibility and accuracy of problem-solving. Moreover, the two-time-scale Markov switching model demonstrated its powerful analytical capabilities in predicting and managing complex systems with memory and long term dependencies, proving its substantial applicative value in handling highly dynamic systems.

Suggested Citation

  • Zhao, Hengzhi & Wu, Qin & Zhang, Jiwei & Lu, Jing & Lv, Dongsheng, 2026. "Averaging principle for stochastic fractional differential equations driven by Tempered Fractional Brownian Motion with two-time-scale Markov switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 367-390.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pa:p:367-390
    DOI: 10.1016/j.matcom.2025.09.003
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    References listed on IDEAS

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    1. Sabzikar, Farzad & Surgailis, Donatas, 2018. "Tempered fractional Brownian and stable motions of second kind," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 17-27.
    2. Xu, Jie, 2022. "An averaging principle for slow–fast fractional stochastic parabolic equations on unbounded domains," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 358-396.
    3. Wang, Ruifang & Xu, Yong & Yue, Hongge, 2022. "Stochastic averaging for the non-autonomous mixed stochastic differential equations with locally Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 182(C).
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