The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds | Zendy

Ehsan Azmoodeh | Zendy; Giovanni Peccati | Zendy; Guillaume Poly | Zendy

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The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds

Author(s) -

Ehsan Azmoodeh,

Giovanni Peccati,

Guillaume Poly

Publication year - 2016

Publication title -

latin american journal of probability and mathematical statistics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.667

H-Index - 18

ISSN - 1980-0436

DOI - 10.30757/alea.v13-26

Subject(s) - law of the iterated logarithm , iterated logarithm , logarithm , gaussian , mathematics , iterated function , statistical physics , pure mathematics , law , mathematical analysis , physics , political science , quantum mechanics

We develop a new method for showing that a given sequence of random variables verifies an appropriate law of the iterated logarithm. Our tools involve the use of general estimates on multidimensional Wasserstein distances, that are in turn based on recently developed inequalities involving Stein matrices and transport distances. Our main application consists in the proof of the exact law of the iterated logarithm for the Hermite variations of a fractional Brownian motion in the critical case.

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