Deviation frequencies of Brownian path property approximations
Probability
2023-09-13 v2
Abstract
This case study proposes robustness quantifications of many classical sample path properties of Brownian motion in terms of the (mean) deviation frequencies along typical a.s.~approximations. 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.
Keywords
Cite
@article{arxiv.2302.04115,
title = {Deviation frequencies of Brownian path property approximations},
author = {Michael A. Högele and Alexander Steinicke},
journal= {arXiv preprint arXiv:2302.04115},
year = {2023}
}
Comments
Correction of constants and adjustments of some examples