Probability Theory/Mathematical Analysis
Local and asymptotic properties of Linear Fractional Stable Sheets
Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 389-394.

In this Note we introduce representations of Linear Fractional Stable Sheets as wavelet random series. Using these representations, in the case where the paths are continuous, an anisotropic uniform and quasi-optimal modulus of continuity of these paths is obtained as well as an upper bound on their behavior at infinity.

Dans cette Note, nous introduisons une représentation du drap linéaire fractionnaire stable sous la forme d'une série aléatoire d'ondelettes. Au moyen de cette représentation, dans le cas où les trajectoires du processus sont continues, un module de continuité anisotropique uniforme quasi-optimal de ces trajectoires est obtenu ainsi qu'un contrôle de leur comportement à l'infini.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.01.017
Ayache, Antoine 1; Roueff, François 2; Xiao, Yimin 3

1 UMR CNRS 8524, laboratoire Paul-Painlevé, bâtiment M2, Université Lille 1, 59655 Villeneuve d'Ascq cedex, France
2 Télécom Paris/CNRS LTCI, 46, rue Barrault, 75634 Paris cedex 13, France
3 Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA
@article{CRMATH_2007__344_6_389_0,
     author = {Ayache, Antoine and Roueff, Fran\c{c}ois and Xiao, Yimin},
     title = {Local and asymptotic properties of {Linear} {Fractional} {Stable} {Sheets}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {389--394},
     publisher = {Elsevier},
     volume = {344},
     number = {6},
     year = {2007},
     doi = {10.1016/j.crma.2007.01.017},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2007.01.017/}
}
TY  - JOUR
AU  - Ayache, Antoine
AU  - Roueff, François
AU  - Xiao, Yimin
TI  - Local and asymptotic properties of Linear Fractional Stable Sheets
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 389
EP  - 394
VL  - 344
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2007.01.017/
DO  - 10.1016/j.crma.2007.01.017
LA  - en
ID  - CRMATH_2007__344_6_389_0
ER  - 
%0 Journal Article
%A Ayache, Antoine
%A Roueff, François
%A Xiao, Yimin
%T Local and asymptotic properties of Linear Fractional Stable Sheets
%J Comptes Rendus. Mathématique
%D 2007
%P 389-394
%V 344
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2007.01.017/
%R 10.1016/j.crma.2007.01.017
%G en
%F CRMATH_2007__344_6_389_0
Ayache, Antoine; Roueff, François; Xiao, Yimin. Local and asymptotic properties of Linear Fractional Stable Sheets. Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 389-394. doi : 10.1016/j.crma.2007.01.017. http://www.numdam.org/articles/10.1016/j.crma.2007.01.017/

[1] Ayache, A.; Xiao, Y. Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets, J. Fourier Anal. Appl., Volume 11 (2005), pp. 407-439

[2] Benassi, A.; Roux, D. Elliptic self-similar stochastic processes, Rev. Mat. Iberoamericana, Volume 19 (2003), pp. 767-796

[3] Bonami, A.; Estrade, A. Anisotropic analysis of some Gaussian models, J. Fourier Anal. Appl., Volume 9 (2003), pp. 215-236

[4] Daubechies, I. Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992

[5] Kôno, N.; Maejima, M. Hölder continuity of sample paths of some self-similar stable processes, Tokyo J. Math., Volume 14 (1991), pp. 93-100

[6] Maejima, M. A self-similar process with nowhere bounded sample paths, Z. Wahrsch. Verw. Gebiete, Volume 65 (1983), pp. 115-119

[7] Meyer, Y. Wavelets and Operators, Cambridge University Press, Cambridge, UK, 1992

[8] Samorodnitsky, G.; Taqqu, M.S. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall, New York, 1994

[9] Takashima, K. Sample path properties of ergodic self-similar processes, Osaka Math. J., Volume 26 (1989), pp. 159-189

Cited by Sources: