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.

中文翻译：

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消失粘度极限下后向随机简并抛物方程的零可控性代价

在本文中，我们研究了在消失粘度极限中具有边界控制的向后随机简并抛物线方程的零可控性成本。首先，我们获得伴随随机方程的新卡尔曼估计。结合卡尔曼估计和指数耗散估计，我们获得了大控制时间的一致零可控性。当等待时间趋于0时，我们证明零可控性成本增加到无穷大。