Abstract
We discuss the method of bounding suprema of canonical processes based on the inclusion of their index set into a convex hull of a well-controlled set of points. While the upper bound is immediate, the reverse estimate was established to date only for a narrow class of regular stochastic processes. We show that for specific index sets, including arbitrary ellipsoids, regularity assumptions may be substantially weakened.
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Supported by the National Science Centre, Poland grant 2015/18/A/ST1/00553.
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Latała, R. (2023). Bounding Suprema of Canonical Processes via Convex Hull. In: Adamczak, R., Gozlan, N., Lounici, K., Madiman, M. (eds) High Dimensional Probability IX. Progress in Probability, vol 80. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-26979-0_13
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DOI: https://doi.org/10.1007/978-3-031-26979-0_13
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