High Dimensional Probability VIII by Nathael Gozlan & Rafał Latała & Karim Lounici & Mokshay Madiman

Author:Nathael Gozlan & Rafał Latała & Karim Lounici & Mokshay Madiman
Language: eng
Format: epub
ISBN: 9783030263911
Publisher: Springer International Publishing

(12.74)

To show the equivalence between (12.73) and (12.74), we follow the discretization method used by Strassen [33] to establish his law of the iterated logarithm. The corresponding details are given in the forthcoming Sect. 12.3.4 for d = 1. Their extension to an arbitrary d ≥ 1 is mostly a matter of book-keeping, with tedious notation for higher dimensions. We will therefore limit ourselves to the essential part of the argument. Consider the modulus of continuity of a n(⋅), defined, for 0 < h ≤ 1, by

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