Abstract In this article, we study the following stochastic heat equation where is the generator of a Lévy process X in B is a fractional-colored Gaussian noise with Hurst index in the time variable and spatial covariance function f which is the Fourier transform of a tempered measure After establishing the existence of solution for the stochastic heat equation, we study the regularity of the solution in both time and space variables. Under mild conditions, we establish the exact uniform modulus of continuity and a Chung-type law of iterated logarithm for the sample function These results, to our knowledge, are new even for the classical stochastic heat equation (where ) with space-time white noise and they strengthen the corresponding results of Balan and Tudor (2008) and Tudor and Xiao (2017) where partial regularity results were obtained.

中文翻译：

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分数色噪声驱动的随机热方程解的锐时空规律

摘要 在本文中，我们研究了以下随机热方程 其中 是 Lévy 过程的发生器 B 中的 X 是分数彩色高斯噪声，时间变量中具有 Hurst 指数，空间协方差函数 f 是回火的傅立叶变换测度 在建立随机热方程解的存在性之后，我们研究解在时间和空间变量上的规律性。在温和的条件下，我们为样本函数建立了精确的均匀连续模量和 Chung 型迭代对数定律 据我们所知，即使对于具有时空白噪声的经典随机热方程（其中 ），这些结果也是新的他们加强了 Balan and Tudor (2008) 和 Tudor and Xiao (2017) 的相应结果，其中获得了部分规律性结果。