  This paper deals with a class of time inconsistent stochastic linear
quadratic (SLQ) optimal control problems in Markovian framework. Three notions,
i.e., closed-loop equilibrium controls/strategies, open-loop equilibrium
controls and their closed-loop representations, are characterized in unified
manners. These results indicate clearer and deeper distinctions among these
notions. For example, in particular time consistent setting, the open-loop
equilibrium controls are fully characterized by first-order, second-order
necessary optimality conditions, and become needlessly optimal, while the
closed-loop equilibrium controls naturally reduce into closed-loop optimal
controls.
