A note on Ritov's Bayes approach to the minimax property of the cusum procedure

Abstract

We consider, in a Bayesian framework, the model Wt = Bt + θ(t -v)+, where B is a standard Brownian motion, θ is arbitrary but known and v is the unknown change-point. We transfer the construction of Ritov to this continuous time setup and show that the corresponding Bayes problems can be reduced to generalized parking problems.