# Erhan Bayraktar - Department of Mathematics, University of Michigan

**Starts:**4:00 pm on Thursday, December 6, 2012

**Ends:**5:00 pm on Thursday, December 6, 2012

**Location:**MCS 148

Title: 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. Joint work with Ross Kravitz.