What question did this study set out to answer?

To explore the turnpike property in non-homogeneous linear stochastic control problems with regime switching.

April 3, 2026

Turnpike property of a linear-quadratic optimal control problem in large horizons with regime switching II: non-homogeneous case

HMHongwei Mei RWRui Adele H WangLanzhou University JYJiongmin Yong

Key Points

To explore the turnpike property in non-homogeneous linear stochastic control problems with regime switching.
Analysis of nonhomogeneous linear stochastic differential equations
Application of quadratic functionals over large time horizons
Extension of previous results on homogeneous linear systems
Established turnpike property for non-homogeneous control problems
Confirmed validity of some results even without regime switching
Demonstrated new findings applicable to broader cases

Abstract

This paper is concerned with an optimal control problem for a nonhomogeneous linear stochastic differential equation having regime switching with a quadratic functional in the large time horizon. This is a continuation of the paper 27, in which the strong turnpike property was established for homogeneous linear systems with purely quadratic cost functionals. We extend the results to the current situation. It turns out that some of the results are new even for the cases without regime switchings.

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