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<p>We generalize the classical Levinson theorem on the asymptotic equivalence on infinite-dimensional stochastic systems. In particular, for a given system of linear stochastic differential equations, we construct a system of ordinary differential equations whose solutions are characterized by the behavior at infinity similar to the behavior of solutions of the original system both in the mean-square sense and with probability 1.</p>

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On the Asymptotic Equivalence of Infinite-Dimensional Stochastic Systems

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Dmytro Shtefan,
  • Oleksandr Stanzhytskyi,
  • Andriy Stanzhytskyi

摘要

We generalize the classical Levinson theorem on the asymptotic equivalence on infinite-dimensional stochastic systems. In particular, for a given system of linear stochastic differential equations, we construct a system of ordinary differential equations whose solutions are characterized by the behavior at infinity similar to the behavior of solutions of the original system both in the mean-square sense and with probability 1.