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<p>This paper investigates the asymptotic behavior of the solution to a linear-quadratic stochastic optimal control problems. The so-called probability cell problem is introduced the first time. It serves as the probability interpretation of the well-known cell problem in the homogenization of Hamilton–Jacobi–Bellman equations. By establishing a connection between this problem and the ergodic cost problem, we reveal the turnpike properties of the linear-quadratic stochastic optimal control problems from various perspectives.</p>

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Long-Time Behaviors of Stochastic Linear-Quadratic Optimal Control Problems

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Jiamin Jian,
  • Sixian Jin,
  • Qingshuo Song,
  • Jiongmin Yong

摘要

This paper investigates the asymptotic behavior of the solution to a linear-quadratic stochastic optimal control problems. The so-called probability cell problem is introduced the first time. It serves as the probability interpretation of the well-known cell problem in the homogenization of Hamilton–Jacobi–Bellman equations. By establishing a connection between this problem and the ergodic cost problem, we reveal the turnpike properties of the linear-quadratic stochastic optimal control problems from various perspectives.