Goran Peskir (University of Manchester) : Optimal Real-Time Detection of a Drifting Brownian Coordinate
2020-03-11 15:00 - 16:00 (Europe/London) | 140, Huxley Building, South Kensington Campus, Imperial College London, London, SW7 2AZ, United Kingdom
Control and Optimisation Seminar

Abstract:
Consider the motion of a Brownian particle in three dimensions,whose two spatial coordinates are standard Brownian motions with zero drift, and the remaining (unknown) spatial coordinate is a standard Brownian motion with a (known) non-zero drift. Given
that the position of the Brownian particle is being observed in real time, the problem is to detect as soon as possible and with minimal probabilities of the wrong terminal decisions, which spatial coordinate has the non-zero drift. We solve this problem in the Bayesian formulation, under any prior probabilities of the non-zero drift being in any of the three spatial coordinates, when the passage of time is penalised linearly. [This is joint work with P. E. Ernst and Q. Zhou.]
