Quickest Search over Brownian Channels
Abstract
In this paper we resolve an open problem proposed by Lai, Poor, Xin, and Georgiadis (2011, IEEE Transactions on Information Theory). Consider a sequence of Brownian Motions with unknown drift equal to one or zero, which we may be observed one at a time. We give a procedure for finding, as quickly as possible, a process which is a Brownian Motion with nonzero drift. This original quickest search problem, in which the filtration itself is dependent on the observation strategy, is reduced to a single filtration impulse control and optimal stopping problem, which is in turn reduced to an optimal stopping problem for a reflected diffusion, which can be explicitly solved.
Keywords
Cite
@article{arxiv.1201.1662,
title = {Quickest Search over Brownian Channels},
author = {Erhan Bayraktar and Ross Kravitz},
journal= {arXiv preprint arXiv:1201.1662},
year = {2013}
}
Comments
To appear in Stochastics. Keywords: Bayesian quickest search, optimal switching, optimal stopping, reflected diffusion