The Cost of Null Controllability for a Backward Stochastic Degenerate Parabolic Equation in the Vanishing Viscosity Limit

In this paper, we investigate the cost of null controllability for a backward stochastic degenerate parabolic equation with a boundary control in the vanishing viscosity limit. Firstly we obtain a new Carleman estimate for the adjoint stochastic equation. Combining this Carleman estimate and an exponential dissipation estimate, we obtain the uniform null controllability for large control time. When the waiting time tends to 0, we prove that the cost of null controllability increases to infinity.