Abstract:This case study proposes a.s.~convergence quantifications of many classical sample path property approximations of Brownian motion in terms of the tradeoff between a.s.~rates and the integrability of the modulus of convergence, as well as the deviation frequencies. This includes Lévy's construction of Brownian motion, the Kolmogorov-Chentsov (and the Kolmogorov-Totoki) continuity theorem, Lévy's modulus of continuity, the Paley-Wiener-Zygmund theorem, the a.s.~approximation of the quadratic variation as well as the laws of the iterated logarithm by Khinchin, Chung and Strassen, among others.
From: Alexander Steinicke [view email]
[v1]
Wed, 8 Feb 2023 15:12:38 UTC (47 KB)
[v2]
Mon, 11 Sep 2023 22:56:57 UTC (48 KB)
[v3]
Sun, 2 Aug 2026 05:06:09 UTC (54 KB)
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