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 Probl. Peredachi Inf., 2012, Volume 48, Issue 2, Pages 65–78 (Mi ppi2075)

Methods of Signal Processing

Sequential estimation of a threshold crossing time for a Gaussian random walk through correlated observations

M. V. Burnasheva, A. Tchamkertenb

a Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow
b Communications and Electronics Department, Télécom ParisTech, France

Abstract: Given a Gaussian random walk $X$ with drift, we consider the problem of estimating its first-passage time $\tau_A$ for a given level $A$ from an observation process $Y$ correlated to $X$. Estimators may be any stopping times $\eta$ with respect to the observation process $Y$. Two cases of the process $Y$ are considered: a noisy version of $X$ and a process $X$ with delay $d$. For a given loss function $f(x)$, in both cases we find exact asymptotics of the minimal possible risk $\mathbf E f((\eta-\tau_A)/r)$ as $A,d\to\infty$, where $r$ is a normalizing coefficient. The results are extended to the corresponding continuous-time setting where $X$ and $Y$ are Brownian motions with drift.

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English version:
Problems of Information Transmission, 2012, 48:2, 142–153

Bibliographic databases:

UDC: 621.391.1+519.2
Revised: 13.04.2012

Citation: M. V. Burnashev, A. Tchamkerten, “Sequential estimation of a threshold crossing time for a Gaussian random walk through correlated observations”, Probl. Peredachi Inf., 48:2 (2012), 65–78; Problems Inform. Transmission, 48:2 (2012), 142–153

Citation in format AMSBIB
\Bibitem{BurTch12} \by M.~V.~Burnashev, A.~Tchamkerten \paper Sequential estimation of a~threshold crossing time for a~Gaussian random walk through correlated observations \jour Probl. Peredachi Inf. \yr 2012 \vol 48 \issue 2 \pages 65--78 \mathnet{http://mi.mathnet.ru/ppi2075} \transl \jour Problems Inform. Transmission \yr 2012 \vol 48 \issue 2 \pages 142--153 \crossref{https://doi.org/10.1134/S0032946012020044} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000306338300004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865763407} 

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• http://mi.mathnet.ru/eng/ppi/v48/i2/p65

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. V. Burnashev, G. K. Golubev, “On limit distributions of the time of first passage over a high level”, Problems Inform. Transmission, 51:2 (2015), 148–164
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