Turnpike properties for stochastic backward linear-quadratic optimal problems

TL;DR

This paper investigates the long-term behavior of solutions to stochastic backward linear-quadratic optimal control problems, establishing conditions under which solutions exhibit turnpike properties, with novel techniques differing from forward cases.

Contribution

It introduces new methods to analyze the turnpike phenomenon in stochastic backward LQ problems, including formulating static problems and correction processes.

Findings

Weak and strong turnpike properties are proven under stabilizability conditions.

The techniques differ significantly from those used in stochastic forward LQ problems.

The results provide insights into the asymptotic behavior of stochastic backward control solutions.

Abstract

This paper deals with the long time behavior of the optimal solution of stochastic backward linear-quadratic optimal control problem over the finite time horizon. Both weak and strong turnpike properties are established under appropriate conditions, including stabilizability condition. The key ingredients are to formulate the corresponding static optimization problem and determine the correction processes. However, our techniques are quite different from stochastic (forward) linear-quadratic case.