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

Jiamin Jian, Sixian Jin, Qingshuo Song, Jiongmin Yong

Published 2024-09-18Version 1

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.