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
Reconstructing a random scenery observed with random errors along a random walk path
Download PDF
Download PDF
  • Published: April 2003

Reconstructing a random scenery observed with random errors along a random walk path

  • Heinrich Matzinger1 &
  • Silke W.W. Rolles2 

Probability Theory and Related Fields volume 125, pages 539–577 (2003)Cite this article

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract.

 We show that an i.i.d. uniformly colored scenery on ℤ observed along a random walk path with bounded jumps can still be reconstructed if there are some errors in the observations. We assume the random walk is recurrent and can reach every point with positive probability. At time k, the random walker observes the color at her present location with probability 1−δ and an error Y k with probability δ. The errors Y k , k≥0, are assumed to be stationary and ergodic and independent of scenery and random walk. If the number of colors is strictly larger than the number of possible jumps for the random walk and δ is sufficiently small, then almost all sceneries can be almost surely reconstructed up to translations and reflections.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. University of Bielefeld, Faculty of Mathematics, Postfach 10 01 31, D-33501 Bielefeld, Germany, e-mail: matzing@mathematik.uni-bielefeld.de, , , , , , DE

    Heinrich Matzinger

  2. University of California, Los Angeles, Department of Mathematics, Box 951555, Los Angeles, CA 90095-1555, USA. e-mail: srolles@math.ucla.edu, , , , , , US

    Silke W.W. Rolles

Authors
  1. Heinrich Matzinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Silke W.W. Rolles
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 3 February 2002 / Revised version: 15 January 2003 Published online: 28 March 2003

Mathematics Subject Classification (2000): 60K37, 60G50

Key words or phrases:Scenery reconstruction – Random walk – Coin tossing problems

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Matzinger, H., Rolles, S. Reconstructing a random scenery observed with random errors along a random walk path. Probab. Theory Relat. Fields 125, 539–577 (2003). https://doi.org/10.1007/s00440-003-0257-3

Download citation

  • Issue Date: April 2003

  • DOI: https://doi.org/10.1007/s00440-003-0257-3

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

  • Color
  • Reflection
  • Random Walk
  • Random Error
  • Positive Probability
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