带一般乘性高斯噪声的随机heat equations：Hölder连续性和不连续性
Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency
摘要：
本文研究了带乘性噪声的随机热方程uW，其中W是平均零高斯噪声，微分元uW在Skorohod和Stratonovich两种意义下都得到了解释.对于具有一般时空协方差结构的噪声，研究了解的存在唯一性。在一般和不同的条件下，得到了解的Feynman-Kac公式和解的矩公式。应用这些公式可以得到解的Hölder连续性。它们也被应用于获得的矩的解的不确定性界。
英文摘要：
This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W is a mean zero Gaussian noise and the differential element uW is interpreted both in the sense of Skorohod and Stratonovich. The existence and uniqueness of the solution are studied for noises with general time and spatial covariance structure. Feynman-Kac formulas for the solutions and for the moments of the solutions are obtained under general and different conditions. These formulas are applied to obtain the Hölder continuity of the solutions. They are also applied to obtain the intermittency bounds for the moments of the solutions.
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