We consider, in a Bayesian framework, the model $W_t = B_t + \theta (t - \nu)^+$, where B is a standard Brownian motion, $\theta$ is arbitrary but known and $\nu$ 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.
"A note on Ritov's Bayes approach to the minimax property of the cusum procedure." Ann. Statist. 24 (4) 1804 - 1812, August 1996. https://doi.org/10.1214/aos/1032298296