SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 563-580, February 2024.
Abstract. In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result [Q. Lü and X Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations, Springer, Cham, Switzerland, 2021], the novelty of this paper is twofold: (1) Our model contains the effects in the drift terms when we put controls directly in the diffusion terms, which is more sensible for practical applications; (2) We provide an explicit description of the waiting time which is sharp in the case of dimension one and is independent of the coefficents of lower terms.

中文翻译：

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精细化随机波方程的精确可控性

SIAM 控制与优化杂志，第 62 卷，第 1 期，第 563-580 页，2024 年 2 月。
摘要。在本文中，我们通过为后向双曲型算子建立一种新颖的卡尔曼估计，获得了具有三个控制的精​​炼随机波动方程的精确可控性。与已知结果比较[Q. Lü 和 X 张，随机偏微分方程的数学控制理论，Springer，Cham，瑞士，2021]，本文的新颖性有两个：（1）当我们将控制直接放入扩散项，这对于实际应用更有意义；(2) 我们提供了等待时间的明确描述，该等待时间在一维情况下是尖锐的，并且与较低项的系数无关。