Let $T$ be a tree with induced partial order. We investigate a centered Gaussian process $X$ indexed by $T$ and generated by weight functions. In a first part we treat general trees and weights and derive necessary and sufficient conditions for the a.s. boundedness of $X$ in terms of compactness properties of $(T,d)$. Here $d$ is a special metric defined by the weights, which, in general, is not comparable with the Dudley metric generated by $X$. In a second part we investigate the boundedness of $X$ for the binary tree. Assuming some mild regularity assumptions about on weight, we completely characterize homogeneous weights with $X$ being a.s. bounded.
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机译：令$ T $为具有部分偏序的树。我们研究由$ T $索引并由权重函数生成的中心高斯过程$ X $。在第一部分中，我们处理通用树和权重，并得出a.s.的必要条件和充分条件。 $ X $的有界性，以$（T，d）$的紧缩性质表示。 $ d $是权重定义的特殊度量，通常与$ X $生成的Dudley度量不具有可比性。在第二部分中，我们研究了二叉树$ X $的有界性。假设关于重量的一些适度规律性假设，我们完全表征均质重量，其中$ X $为a.s。有界。
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