English

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

Optimization and Control 2026-02-25 v2

Abstract

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 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.

Keywords

Cite

@article{arxiv.2409.11633,
  title  = {Long-Time Behaviors of Stochastic Linear-Quadratic Optimal Control Problems},
  author = {Jiamin Jian and Sixian Jin and Qingshuo Song and Jiongmin Yong},
  journal= {arXiv preprint arXiv:2409.11633},
  year   = {2026}
}

Comments

35 pages

R2 v1 2026-06-28T18:48:30.498Z