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Strong convergence in averaging principle for stochastic hyperbolic–parabolic equations with two time-scales

Author

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  • Fu, Hongbo
  • Wan, Li
  • Liu, Jicheng

Abstract

This article deals with averaging principle for stochastic hyperbolic–parabolic equations with slow and fast time-scales. Under suitable conditions, the existence of an averaging equation eliminating the fast variable for this coupled system is proved. As a consequence, an effective dynamics for slow variable which takes the form of stochastic wave equation is derived. Also, the rate of strong convergence for the slow component towards the solution of the averaging equation is obtained as a byproduct.

Suggested Citation

  • Fu, Hongbo & Wan, Li & Liu, Jicheng, 2015. "Strong convergence in averaging principle for stochastic hyperbolic–parabolic equations with two time-scales," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3255-3279.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:8:p:3255-3279
    DOI: 10.1016/j.spa.2015.03.004
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    Cited by:

    1. 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.
    2. Bréhier, Charles-Edouard, 2020. "Orders of convergence in the averaging principle for SPDEs: The case of a stochastically forced slow component," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3325-3368.
    3. Fu, Hongbo & Wan, Li & Liu, Jicheng & Liu, Xianming, 2018. "Weak order in averaging principle for stochastic wave equation with a fast oscillation," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2557-2580.
    4. Li, Butong & Meng, Yongna & Sun, Xiaobin & Yang, Ting, 2022. "Optimal strong convergence rate for a class of McKean–Vlasov SDEs with fast oscillating perturbation," Statistics & Probability Letters, Elsevier, vol. 191(C).

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