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

H. Matzinger, S.W.W. Rolles

    Research output: Contribution to journalArticleAcademicpeer-review

    14 Citations (Scopus)

    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-d and an error Y k with probability d. 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 d is sufficiently small, then almost all sceneries can be almost surely reconstructed up to translations and reflections.
    Original languageEnglish
    Pages (from-to)539-577
    JournalProbability Theory and Related Fields
    Volume125
    Issue number4
    DOIs
    Publication statusPublished - 2003

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