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<p>We prove that the asymptotic stability, also known as the weak mixing, is equivalent to a lower bound condition together with the eventual continuity. The latter is a form of weak regularity for Markov–Feller semigroups that generalizes the e-property. Additionally, we provide an example of an asymptotically stable Markov semigroup with essential randomness that does not satisfy the e-property.</p>

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Asymptotic Stability for Non-equicontinuous Markov Semigroups

  • 期刊论文

  • 发表日期：

    2025年6月9日

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  • Fuzhou Gong,
  • Yong Liu,
  • Yuan Liu,
  • Ziyu Liu

摘要

We prove that the asymptotic stability, also known as the weak mixing, is equivalent to a lower bound condition together with the eventual continuity. The latter is a form of weak regularity for Markov–Feller semigroups that generalizes the e-property. Additionally, we provide an example of an asymptotically stable Markov semigroup with essential randomness that does not satisfy the e-property.