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Asymptotic Behavior of Stochastic Complex Lattice Systems Driven by Superlinear Noise

Author

Listed:
  • Zhang Chen

    (Shandong University)

  • Bixiang Wang

    (New Mexico Institute of Mining and Technology)

Abstract

This paper deals with the asymptotic behavior of complex stochastic lattice systems driven by superlinear noise. We first prove the well-posedness and the existence of weak mean random attractors of the systems. We then show the existence of periodic measures and the weak compactness of the set of all periodic measures when a parameter varies in a bounded interval. We finally examine the limiting behavior of the periodic measures and in particular prove that every limit of periodic measures of the stochastic Ginzburg–Landau lattice system must be a periodic measure of the stochastic Schrödinger lattice system.

Suggested Citation

  • Zhang Chen & Bixiang Wang, 2023. "Asymptotic Behavior of Stochastic Complex Lattice Systems Driven by Superlinear Noise," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1487-1519, September.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:3:d:10.1007_s10959-022-01206-9
    DOI: 10.1007/s10959-022-01206-9
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    References listed on IDEAS

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    1. Oleksandr Misiats & Oleksandr Stanzhytskyi & Nung Kwan Yip, 2016. "Existence and Uniqueness of Invariant Measures for Stochastic Reaction–Diffusion Equations in Unbounded Domains," Journal of Theoretical Probability, Springer, vol. 29(3), pages 996-1026, September.
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