Sequential Testing Problems for Bessel Processes

Research output: Contribution to journalArticle


Consider the motion of a Brownian particle that takes place either in a two-dimensional plane or in three-dimensional space. Given that only the distance of the particle to the origin is being observed, the problem is to detect the true dimension as soon as possible and with minimal probabilities of the wrong terminal decisions. We solve this problem in the Bayesian formulation under any prior probability of the true dimension when the passage of time is penalised linearly.

Bibliographical metadata

Original languageEnglish
Pages (from-to)2085-2113
Number of pages29
JournalTransactions of the American Mathematical Society
Early online date8 Sep 2017
StatePublished - 2018