Bruno Buonaguidi - An optimal sequential procedure for determining the drift of a Brownian motion among three values
|Starts:||15:00 12 May 2021|
|Ends:||16:00 12 May 2021|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
Bruno Buonaguidi (Università Cattolica del Sacro Cuore) will speak in the Probability seminar.
Consider the motion of a Brownian particle in one dimension, having a random and unobservable drift which can take one of three known values. Given that we monitor the position of the Brownian particle in real time, the problem is to determine as soon as possible and with minimal probabilities of the wrong terminal decisions, which value the drift has taken. We derive the exact solution to the problem in the Bayesian formulation, under any prior probability distribution on the three values that the drift can assume, when the passage of time is penalized linearly. Unlike most of the sequential testing problems analyzed to date, the optimal stopping boundaries of the present problem are non-monotone.
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