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<p>We obtain sufficient conditions for the uniqueness of a probability solution to the stationary Kolmogorov equation with a degenerate diffusion matrix. We employ the method of doubling variables known in stochastic analysis directly to the Kolmogorov equation.</p>

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Doubling Variables and Uniqueness of Probability Solutions to Degenerate Stationary Kolmogorov Equations

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Vladimir I. Bogachev,
  • Stanislav V. Shaposhnikov,
  • Dmitry V. Shatilovich

摘要

We obtain sufficient conditions for the uniqueness of a probability solution to the stationary Kolmogorov equation with a degenerate diffusion matrix. We employ the method of doubling variables known in stochastic analysis directly to the Kolmogorov equation.