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

Abstract

Given a Gaussian random walkX with drift, we consider the problem of estimating its first-passage time τA 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 − τA)/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. DOI: 10.1134/S0032946012020044

DOI: 10.1134/S0032946012020044

Cite this paper

@article{Burnashev2012SequentialEO, title={Sequential estimation of a threshold crossing time for a Gaussian random walk through correlated observations}, author={Marat V. Burnashev and Aslan Tchamkerten}, journal={Probl. Inf. Transm.}, year={2012}, volume={48}, pages={142-153} }