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<p>This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise. The existence of invariant measures is established using the classical Krylov-Bogoliubov theory. The uniqueness of invariant measures and the weak convergence of transition probabilities are demonstrated through the application of the asymptotic coupling method and Foias-Prodi estimate.</p>

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Ergodicity and weak convergence of transition probabilities for the 2D primitive equations with multiplicative noise

  • 期刊论文

  • 发表日期：

    2025年10月29日

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  • Jintao Li,
  • Hongjun Gao

摘要

This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise. The existence of invariant measures is established using the classical Krylov-Bogoliubov theory. The uniqueness of invariant measures and the weak convergence of transition probabilities are demonstrated through the application of the asymptotic coupling method and Foias-Prodi estimate.