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Detecting a local perturbation in a continuous scenery
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Heinrich Matzinger, Georgia Institute of Technology
Serguei Popov, Universidade de São Paulo
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Abstract
A continuous one-dimensional scenery is a double-infinite sequence of points (thought of as locations of bells) in R. Assume that a scenery X
is observed along the path of a Brownian motion in the following way:
when the Brownian motion encounters a bell different from the last one
visited, we hear a ring. The trajectory of the Brownian motion is
unknown, whilst the scenery X
is known except in some finite interval. We prove that given only the
sequence of times of rings, we can a.s. reconstruct the scenery X entirely. For this we take the scenery X to be a local perturbation of a Poisson scenery X'. We
present an explicit reconstruction algorithm. This problem is the
continuous analog of the "detection of a defect in a discrete
scenery". Many of the essential techniques used with discrete
sceneries do not work with continuous sceneries.
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Full text: PDF
Pages: 637-660
Published on: May 13, 2007
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Electronic Journal of Probability. ISSN: 1083-6489 |
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