We prove the existence and uniqueness of the solutions to a Caputo–Hadamard fractional stochastic differential equation driven by a multiplicative white noise, which may describe the random phenomena in the ultraslow diffusion processes. The moment estimates are given in terms of the logarithmic Mittag–Leffler function. We also prove the regularity of the solutions via the logarithmic Hölder continuity.

中文翻译：

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Caputo-Hadamard 分数阶随机微分方程的适定性和正则性

我们证明了由乘法白噪声驱动的 Caputo-Hadamard 分数阶随机微分方程解的存在性和唯一性，它可以描述超慢扩散过程中的随机现象。矩估计是根据对数 Mittag-Leffler 函数给出的。我们还通过对数 Hölder 连续性证明了解的规律性。