Stackelberg–Nash Null Controllability for Stochastic Parabolic Equations

ABSTRACT We study a hierarchical control problem for stochastic parabolic equations that involve a gradient term in the drift part. We employ the Stackelberg–Nash strategy with two leaders and two followers. The leaders are responsible for selecting the policy targeting null controllability, while the followers solve a bi‐objective optimal control problem which consists of maintaining the solution process close to prefixed targets. Once the Nash equilibrium is determined, the problem reduces to achieving null controllability of a coupled forward‐backward stochastic system. To solve this problem, via Carleman estimates, we establish a suitable observability inequality. Subsequently, we achieve the desired controllability result.