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

Sequential estimation of a threshold crossing time for a Gaussian random walk through correlated... Given a Gaussian random walk X with drift, we consider the problem of estimating its first-passage time τ A for a given level A from an observation process Y correlated to X. Estimators may be any stopping times η 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 E f((η − τ A )/r) as A, d → ∞, 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

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

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2012 by Pleiades Publishing, Ltd.
Subject
Engineering; Information Storage and Retrieval; Systems Theory, Control; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946012020044
Publisher site
See Article on Publisher Site

Abstract

Given a Gaussian random walk X with drift, we consider the problem of estimating its first-passage time τ A for a given level A from an observation process Y correlated to X. Estimators may be any stopping times η 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 E f((η − τ A )/r) as A, d → ∞, 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.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 13, 2012

References

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