Turnpike properties for stochastic backward linear-quadratic optimal problems

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.