论文标题
双曲线随机部分微分方程的溶液的Malliavin可不同性，不规则漂移
Malliavin differentiability of solutions of hyperbolic stochastic partial differential equations with irregular drifts
论文作者
论文摘要
当漂移系数是两个组合单调的单调硼孔的差异时，我们证明了对双曲线随机部分微分方程的解决方案的路径唯一性。然后，由布朗尼纸驱动的SDE的Yamada-Watanabe原理允许对这种方程式获得强大的独特性，从而扩展了[Bogso，Dieye和Menoukeu Pamen，Elect的结果。 J. Probab。，27：1-26，2022]和[Nualart和Tindel，潜在的肛门，7（3）：661---680，1997]。假设漂移是全球界限的，我们表明独特的强溶液是Malliavin可区分的。还研究了空间线性生长漂移系数的情况。
We prove path-by-path uniqueness of solution to hyperbolic stochastic partial differential equations when the drift coefficient is the difference of two componentwise monotone Borel measurable functions of spatial linear growth. The Yamada-Watanabe principle for SDE driven by Brownian sheet then allows to derive strong uniqueness for such equation and thus extending the results in [Bogso, Dieye and Menoukeu Pamen, Elect. J. Probab., 27:1-26, 2022] and [Nualart and Tindel, Potential Anal., 7(3):661--680, 1997]. Assuming that the drift is globally bounded, we show that the unique strong solution is Malliavin differentiable. The case of spatial linear growth drift coefficient is also studied.
