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- W2001567961 abstract "Initially we consider the standard isonormal linear process $L$ on a Hilbert space $H$, and applying metric entropy methods obtain bounds for the probability that $sup_CLx > lambda, C subset H$ and $lambda$ large. Under the assumption that the entropy function of $C$ grows polynomially, we find bounds of the form $clambda^alphaexp(- frac{1}{2}lambda^2/sigma^2)$, where $sigma^2$ is the maximal variance of $L$. We use a notion of entropy finer than that usually employed and specifically suited to the nonstationary situation. As a result we obtain, in the nonstationary setting, more precise bounds than any in the literature. We then treat a number of examples in which the power $alpha$ is identified. These include the distributions of the maxima of the rectangle indexed, pinned Brownian sheet on $mathbb{R}^k$ for which $alpha = 2(2k - 1)$, and the half plane indexed pinned sheet on $mathbb{R}^2$ for which $alpha = 2$." @default.
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- W2001567961 date "1987-10-01" @default.
- W2001567961 modified "2023-10-15" @default.
- W2001567961 title "Tail Behaviour for the Suprema of Gaussian Processes with Applications to Empirical Processes" @default.
- W2001567961 doi "https://doi.org/10.1214/aop/1176991980" @default.
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