@article{EJP409,
author = {Heinrich Matzinger and Serguei Popov},
title = {Detecting a Local Perturbation in a Continuous Scenery},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {12},
year = {2007},
keywords = {Brownian motion, Poisson process, localization test, detecting defects in sceneries seen along random walks},
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.},
pages = {no. 22, 637-660},
issn = {1083-6489},
doi = {10.1214/EJP.v12-409},
url = {http://ejp.ejpecp.org/article/view/409}}