Some distributional properties of the continuous wavelet transform of random processes

被引：9
|
作者：
Averkamp, R [1 ]
Houdre, C
机构：
[1] Univ Freiburg, Inst Math Stochastik, D-79104 Freiburg, Germany
[2] Georgia Inst Technol, Sch Math, SE Appl Anal Ctr, Atlanta, GA 30332 USA
[3] Georgia Inst Technol, Sch Math, Ctr Appl Probabil, Atlanta, GA 30332 USA
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 1998年 / 44卷 / 03期
基金：
美国国家科学基金会;
关键词：
fractional Brownian fields; random fields; random processes; wavelet transform;
D O I：
10.1109/18.669179
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Without finite moment conditions, some properties of random processes, such as stationarity and self-similarity, are characterized iia corresponding properties of their wavelet transform. Anyone of these distributional properties of the wavelet transform characterizes the corresponding property of the increments of the random process, of order equal to the order of regularity of the analyzing wavelet. Extensions of these results to random fields are then indicated.
引用
收藏
页码：1111 / 1124
页数：14
相关论文
共 50 条
  • [21] Distributional properties of continuous time processes: from CIR to bates
    Okhrin, Ostap
    Rockinger, Michael
    Schmid, Manuel
    [J]. ASTA-ADVANCES IN STATISTICAL ANALYSIS, 2023, 107 (03) : 397 - 419
  • [22] Local regularity properties of continuous wavelet transform in n dimensions
    Tang, Raosheng
    [J]. Hunan Daxue Xuebao/Journal of Hunan University Natural Sciences, 1995, 22 (04):
  • [23] Classification of Heart Sounds using Discrete and Continuous Wavelet Transform and Random Forests
    Balili, Christine C.
    Sobrepena, Ma. Caryssa C.
    Naval, Prospero C., Jr.
    [J]. PROCEEDINGS 3RD IAPR ASIAN CONFERENCE ON PATTERN RECOGNITION ACPR 2015, 2015, : 655 - 659
  • [24] Effectiveness of the continuous wavelet transform in the analysis of some dispersive elastic waves
    Kim, YY
    Kim, EH
    [J]. JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2001, 110 (01): : 86 - 94
  • [25] The continuous wavelet transform with rotations
    Jaime Navarro
    Miguel Angel Alvarez
    [J]. Sampling Theory in Signal and Image Processing, 2005, 4 (1): : 45 - 55
  • [26] Instantaneous parameter estimation based on continuous wavelet transform and some improvements
    Zhang, HF
    Zhao, JP
    Huang, JG
    [J]. PROCEEDINGS OF THE 1998 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, VOLS 1-6, 1998, : 2169 - 2172
  • [27] Continuous wavelet transform - An introduction
    Ojha, A
    [J]. WAVELETS AND ALLIED TOPICS, 2001, : 1 - 13
  • [28] Images of the continuous wavelet transform
    Ghandehari, Mahya
    Taylor, Keith F.
    [J]. OPERATOR METHODS IN WAVELETS, TILINGS, AND FRAMES, 2014, 626 : 55 - 65
  • [29] The Inverse of the Continuous Wavelet Transform
    Weisz, Ferenc
    [J]. COMPUTER AIDED SYSTEMS THEORY - EUROCAST 2017, PT II, 2018, 10672 : 246 - 253
  • [30] Continuous wavelet transform on the hyperboloid
    Bogdanova, Iva
    Vandergheynst, Pierre
    Gazeau, Jean-Pierre
    [J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2007, 23 (03) : 285 - 306
12345