 Reconstruction of periodic sceneries seen along a random walkHeinrich Matzinger and Jüri Lember Stochastic Processes and their Applications, 2006, vol. 116, issue 11, 1584-1599 Abstract: This article was motivated by a question of Kesten. Kesten asked for which random walks periodic sceneries can be reconstructed. Among others, he asked the question for random walks which at each step can move by one or two units to the right. Previously, Howard [C.D. Howard, Distinguishing certain random sceneries on via random walks, Statist. Probab. Lett. 34 (2) (1997) 123-132] proved that all periodic sceneries can be reconstructed provided they are observed along the path of a simple random walk. We prove that for a large class of random walks it is possible to reconstruct periodic sceneries. Among others, we consider the random walk that can only move by one or two units to the right at each step. We show that in this case, the scenery can be reconstructed, provided that the two unit step is less likely than the one unit step. Keywords: Scenery; reconstruction; Random; walk (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:116:y:2006:i:11:p:1584-1599 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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