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.
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@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://archive.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://archive.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://archive.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://archive.numdam.org/articles/10.1016/j.crma.2007.01.017/
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