Deviation frequencies of Brownian path property approximations

Michael A. Högele; Alexander Steinicke

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arXiv · 2302.04115

Deviation frequencies of Brownian path property approximations

Michael A. Högele·Alexander Steinicke

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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 L\'evy's construction of Brownian motion, the Kolmogorov-Chentsov (and the Kolmogorov-Totoki) continuity theorem, L\'evy'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.

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Michael A. Högele, Alexander Steinicke. 2023-02-08. Deviation frequencies of Brownian path property approximations. https://arxiv.org/abs/2302.04115

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