On lacunary wavelet series

被引：61
|
作者：
Jaffard, S [1 ]
机构：
[1] Univ Paris 12, Fac Sci & Technol, Dept Math, F-94010 Creteil, France
来源：
ANNALS OF APPLIED PROBABILITY | 2000年 / 10卷 / 01期
关键词：
wavelet bases; Hausdorff dimensions; chirps; Holder regularity; modulus of continuity;
D O I：
10.1214/aoap/1019737675
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We prove that the Holder singularities of random lacunary wavelet series are chirps located on random fractal sets. We determine the Hausdorff dimensions of these singularities, and the a.e. modulus of continuity of the series. Lacunary wavelet series thus turn out to be a new example of multifractal functions.
引用
收藏
页码：313 / 329
页数：17
相关论文
共 50 条
  • [41] Behavior of lacunary series at the natural boundary
    Costin, O.
    Huang, M.
    ADVANCES IN MATHEMATICS, 2009, 222 (04) : 1370 - 1404
  • [42] ON LACUNARY FOURIER SERIES .2.
    XIE, TF
    CHINESE MATHEMATICS, 1966, 8 (04): : 534 - &
  • [43] INTEGRABILITY OF LACUNARY TRIGONOMETRIC SERIES WITH WEIGHT
    TELJAKOVSKII, SA
    ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1979, 33 (1-2): : 217 - 222
  • [44] A series of lacunary Fouriers - Inverse theorems
    Wiener, N
    Mandelbrojt, S
    COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1936, 203 : 233 - 234
  • [45] ON LACUNARY TRIGONOMETRIC SERIES .2.
    TAKAHASHI, S
    PROCEEDINGS OF THE JAPAN ACADEMY, 1968, 44 (08): : 766 - +
  • [46] ON THE COEFFICIENTS OF LACUNARY POWER-SERIES
    ANDERSON, JM
    NEWMAN, DJ
    QUARTERLY JOURNAL OF MATHEMATICS, 1981, 32 (125): : 1 - 9
  • [47] On the class of limits of lacunary trigonometric series
    C. Aistleitner
    Acta Mathematica Hungarica, 2010, 129 : 1 - 23
  • [48] Irregular discrepancy behavior of lacunary series
    Christoph Aistleitner
    Monatshefte für Mathematik, 2010, 160 : 1 - 29
  • [49] PROBABILISTIC BEHAVIOR OF SOME LACUNARY SERIES
    HAWKES, J
    ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1980, 53 (01): : 21 - 33
  • [50] Irregular discrepancy behavior of lacunary series
    Aistleitner, Christoph
    MONATSHEFTE FUR MATHEMATIK, 2010, 160 (01): : 1 - 29
12345