Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Construction of stationary self-similar generalized fields by random wavelet expansion
Download PDF
Download PDF
  • Published: October 2001

Construction of stationary self-similar generalized fields by random wavelet expansion

  • Zhiyi Chi1 

Probability Theory and Related Fields volume 121, pages 269–300 (2001)Cite this article

  • 71 Accesses

  • 7 Citations

  • Metrics details

Abstract.

Random wavelet expansion is introduced in the study of stationary self-similar generalized random fields. It is motivated by a model of natural images, in which 2D views of objects are randomly scaled and translated because the objects are randomly distributed in the 3D space. It is demonstrated that any stationary self-similar random field defined on the dual space of a Schwartz space of smooth rapidly decreasing functions has a random wavelet expansion representation. To explicitly construct stationary self-similar random fields, random wavelet expansion representations incorporating random functionals of the following three types are considered: (1) a multiple stochastic integral over the product domain of scale and translate, (2) an iterated one, first integrating over the scale domain, and (3) an iterated one, first integrating over the translate domain. We show that random wavelet expansion gives rise to a variety of stationary self-similar random fields, including such well-known processes as the linear fractional stable motions.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Department of Statistics, The University of Chicago, Chicago, IL 60637, USA. e-mail: chi@galton.uchicago.edu, , , , , , US

    Zhiyi Chi

Authors
  1. Zhiyi Chi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 11 December 1998 / Revised version: 31 January 2001 / Published online: 23 August 2001

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chi, Z. Construction of stationary self-similar generalized fields by random wavelet expansion. Probab Theory Relat Fields 121, 269–300 (2001). https://doi.org/10.1007/PL00008805

Download citation

  • Issue Date: October 2001

  • DOI: https://doi.org/10.1007/PL00008805

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Random Field
  • Dual Space
  • Natural Image
  • Generalize Field
  • Stable Motion
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature