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arXiv · 2409.11633

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

Jiamin Jian·Sixian Jin·Qingshuo Song·Jiongmin Yong
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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.

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Jiamin Jian, Sixian Jin, Qingshuo Song, Jiongmin Yong. 2024-09-18. Long-Time Behaviors of Stochastic Linear-Quadratic Optimal Control Problems. https://arxiv.org/abs/2409.11633

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