A uniform dimension result for two-dimensional fractional multiplicative processes

Xiong Jin

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 2, page 512-523
  • ISSN: 0246-0203

Abstract

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Given a two-dimensional fractional multiplicative process ( F t ) t ∈ [ 0 , 1 ] determined by two Hurst exponents H 1 and H 2 , we show that there is an associated uniform Hausdorff dimension result for the images of subsets of [ 0 , 1 ] by F if and only if H 1 = H 2 .

How to cite

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Jin, Xiong. "A uniform dimension result for two-dimensional fractional multiplicative processes." Annales de l'I.H.P. Probabilités et statistiques 50.2 (2014): 512-523. <http://eudml.org/doc/271995>.

@article{Jin2014,
abstract = {Given a two-dimensional fractional multiplicative process $(F_\{t\})_\{t\in [0,1]\}$ determined by two Hurst exponents $H_\{1\}$ and $H_\{2\}$, we show that there is an associated uniform Hausdorff dimension result for the images of subsets of $[0,1]$ by $F$ if and only if $H_\{1\}=H_\{2\}$.},
author = {Jin, Xiong},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Hausdorff dimension; fractional multiplicative processes; uniform dimension result; level sets},
language = {eng},
number = {2},
pages = {512-523},
publisher = {Gauthier-Villars},
title = {A uniform dimension result for two-dimensional fractional multiplicative processes},
url = {http://eudml.org/doc/271995},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Jin, Xiong
TI - A uniform dimension result for two-dimensional fractional multiplicative processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 2
SP - 512
EP - 523
AB - Given a two-dimensional fractional multiplicative process $(F_{t})_{t\in [0,1]}$ determined by two Hurst exponents $H_{1}$ and $H_{2}$, we show that there is an associated uniform Hausdorff dimension result for the images of subsets of $[0,1]$ by $F$ if and only if $H_{1}=H_{2}$.
LA - eng
KW - Hausdorff dimension; fractional multiplicative processes; uniform dimension result; level sets
UR - http://eudml.org/doc/271995
ER -

References

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