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- W4297079172 abstract "Let $T$ be a tree with induced partial order $preceq$. We investigate centered Gaussian processes $X=(X_t)_{tin T}$ represented as $$ X_t=sigma(t)sum_{v preceq t}alpha(v)xi_v $$ for given weight functions $alpha$ and $sigma$ on $T$ and with $(xi_v)_{vin T}$ i.i.d. standard normal. 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 via $alpha$ and $sigma$, 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 and for homogeneous weights. Assuming some mild regularity assumptions about $alpha$ we completely characterize weights $alpha$ and $sigma$ with $X$ being a.s. bounded." @default.
- W4297079172 created "2022-09-26" @default.
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- W4297079172 date "2010-12-13" @default.
- W4297079172 modified "2023-09-27" @default.
- W4297079172 title "Random Gaussian sums on trees" @default.
- W4297079172 doi "https://doi.org/10.48550/arxiv.1012.2683" @default.
- W4297079172 hasPublicationYear "2010" @default.
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