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- W2904673162 abstract "In this paper we improve Bernoulli comparison. The result works for independent Rademacher random variables $(varepsilon_i)_{igeq1}$ and states that we can compare $mathbb{E}sup_{tin T}sum_{igeq1}varphi_{i}(t)varepsilon_i$ with $mathbb{E}sup_{tin T}sum_{igeq1}t_ivarepsilon_i$, where a function $varphi=(varphi_i)_{igeq1}: ell^2supset Trightarrowell^2$, satisfies certain conditions. Originally, it is assumed that each of $varphi_i$ is a contraction. We relax this assumption towards comparison of Gaussian parts of increments, which can be described in the following way. For all $s,tin T$, $pgeq 0$ $$ inf_{|I^c|leq Cp}sum_{iin I}|varphi_i(t)-varphi_i(s)|^2leq C^2inf_{|I^c|leq p}sum_{iin I}|t_i-s_i|^2, $$ where $Cgeq 1$ is an absolute constant and $Isubsetmathbb{N}$, $I^c=mathbb{N}backslash I$." @default.
- W2904673162 created "2018-12-22" @default.
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- W2904673162 date "2018-12-11" @default.
- W2904673162 modified "2023-09-27" @default.
- W2904673162 title "On a contraction property of Bernoulli canonical processes" @default.
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