We analyze the solution to the linear stochastic heat equation driven by a multiparameter Hermite process of order [Formula: see text]. This solution is an element of the [Formula: see text]th Wiener chaos. We discuss various properties of the solution, such as the necessary and sufficient condition for its existence, self-similarity, [Formula: see text]-variation and regularity of its sample paths. We will also focus on the probability distribution of the solution, which is non-Gaussian when [Formula: see text].

中文翻译：

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带有 Hermite 噪声的线性随机热方程

我们分析了由多参数 Hermite 阶过程驱动的线性随机热方程的解 [公式：见正文]。这个解决方案是[公式：见正文]维纳混沌的一个元素。我们讨论了解的各种性质，例如其存在的充要条件、自相似性、[公式：见正文]-其样本路径的变化和规律性。我们还将关注解的概率分布，它是非高斯的[公式：见正文]。