Law of the iterated logarithm type results for random vectors with infinite second moments

Uwe Einmahl

Mathematica Applicanda (2016)

  • Volume: 44, Issue: 1
  • ISSN: 1730-2668

Abstract

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This survey paper is an extended version of the author’s presentation at the conference in honor of Professor F. Thomas Bruss at the occasion of his retirement as Chair of Math´ematiques G´en´erales from the Unversit´e Libre de Bruxelles which was held September 9-11, 2015 in Brussels. I first present some results generalizing the classical Hartman-Wintner law of the iterated logarithm to 1-dimensional variables with infinite second moments and then I show how these results can be further extended to the d-dimensional setting. Finally, I look at general functional law of the iterated logarithm type results.

How to cite

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Uwe Einmahl. "Law of the iterated logarithm type results for random vectors with infinite second moments." Mathematica Applicanda 44.1 (2016): null. <http://eudml.org/doc/292973>.

@article{UweEinmahl2016,
abstract = {This survey paper is an extended version of the author’s presentation at the conference in honor of Professor F. Thomas Bruss at the occasion of his retirement as Chair of Math´ematiques G´en´erales from the Unversit´e Libre de Bruxelles which was held September 9-11, 2015 in Brussels. I first present some results generalizing the classical Hartman-Wintner law of the iterated logarithm to 1-dimensional variables with infinite second moments and then I show how these results can be further extended to the d-dimensional setting. Finally, I look at general functional law of the iterated logarithm type results.},
author = {Uwe Einmahl},
journal = {Mathematica Applicanda},
keywords = {Hartman-Wintner LIL, functional LIL, infinite variance, LIL behavior, very slowly varying function, cluster sets, strong invariance principle.},
language = {eng},
number = {1},
pages = {null},
title = {Law of the iterated logarithm type results for random vectors with infinite second moments},
url = {http://eudml.org/doc/292973},
volume = {44},
year = {2016},
}

TY - JOUR
AU - Uwe Einmahl
TI - Law of the iterated logarithm type results for random vectors with infinite second moments
JO - Mathematica Applicanda
PY - 2016
VL - 44
IS - 1
SP - null
AB - This survey paper is an extended version of the author’s presentation at the conference in honor of Professor F. Thomas Bruss at the occasion of his retirement as Chair of Math´ematiques G´en´erales from the Unversit´e Libre de Bruxelles which was held September 9-11, 2015 in Brussels. I first present some results generalizing the classical Hartman-Wintner law of the iterated logarithm to 1-dimensional variables with infinite second moments and then I show how these results can be further extended to the d-dimensional setting. Finally, I look at general functional law of the iterated logarithm type results.
LA - eng
KW - Hartman-Wintner LIL, functional LIL, infinite variance, LIL behavior, very slowly varying function, cluster sets, strong invariance principle.
UR - http://eudml.org/doc/292973
ER -

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