Optimal Real-time Detection of a Drifting Brownian Coordinate and Statistical Inference for Paths of Stochastic Processes
Philip Ernst, Rice University, USA
Consider a three-dimensional Brownian motion whose two coordinate processes are standard Brownian motions with zero drift,
and the third (unknown) coordinate process is a standard Brownian motion with a non-zero drift. Given that only the position of the
three-dimensional Brownian motion X is being observed, the problem is to detect, as soon as possible and with minimal probabilities of
the wrong terminal decisions, which coordinate process 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 coordinates when the passage of time is penalized linearly.
Time permitting, we will then briefly discuss how we recently resolved a longstanding open statistical problem. The problem,
formulated by the British statistician Udny Yule in 1926, is to mathematically prove Yule's 1926 empirical finding of "nonsense correlation".
The solution of this problem has prompted our recent investigation into tests of independence for paths of stochastic processes.