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<p>We study the long-term behavior of sub-stationary Markov processes, mainly including establishing the functional law of large numbers, the functional central limit theorem, and the quasi-stationary theorem for them. For symmetric Markov processes, we give a precise characterization of the parameters related to their long-term behavior. Finally, we provide easy-to-check conditions that ensure the satisfactory long-term behavior of the Feynman-Kac subprocesses derived from symmetric Markov processes killed by multiplicative functionals.</p>

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On the Long-term Behavior for Sub-stationary Markov Processes

  • 期刊论文

  • 发表日期：

    2025年8月13日

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  • Huasheng Li,
  • Wen Qin,
  • Hanjun Zhang

摘要

We study the long-term behavior of sub-stationary Markov processes, mainly including establishing the functional law of large numbers, the functional central limit theorem, and the quasi-stationary theorem for them. For symmetric Markov processes, we give a precise characterization of the parameters related to their long-term behavior. Finally, we provide easy-to-check conditions that ensure the satisfactory long-term behavior of the Feynman-Kac subprocesses derived from symmetric Markov processes killed by multiplicative functionals.