 Reconstruction of sceneries with correlated colorsMatthias Löwe and Heinrich Matzinger Stochastic Processes and their Applications, 2003, vol. 105, issue 2, 175-210 Abstract: Matzinger (Random Structure Algorithm 15 (1999a) 196) showed how to reconstruct almost every three color scenery, that is a coloring of the integers with three colors, by observing it along the path of a simple random walk, if this scenery is the outcome of an i.i.d. process. This reconstruction needed among others the transience of the representation of the scenery as a random walk on the three-regular tree T3. Den Hollander (private communication) asked which conditions are necessary to ensure this transience of the representation of the scenery as a random walk on T3 and whether this already suffices to make the reconstruction techniques in Matzinger (1999a) work. In this note we answer the latter question in the affirmative. Also we exhibit a large class of examples where the above-mentioned transience holds true. Some counterexamples show that in some sense the given class of examples is the largest natural class with the property that the representation of the scenery as a random walk is transient. Keywords: Scenery; reconstruction; Random; walks; Ergodic; theory (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:105:y:2003:i:2:p:175-210 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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