This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Gapeev, Pavel2016-03-242019-06-2820060946-8633https://doi.org/10.34657/2753https://oa.tib.eu/renate/handle/123456789/2150We study nonadditive Bayesian problems of detecting a change in drift of an observed diffusion process where the cost function of the detection delay has the same structure as in [27] and construct a finite-dimensional Markovian sufficient statistic for that case. We show that when the cost function is linear the optimal stopping time is found as the first time when the a posteriori probability process hits a stochastic boundary depending on the observation process. It is shown that under some nontrivial relationships on the coefficients of the observed diffusion the problem admits a closed form solution. The method of proof is based on embedding the initial problem into a two-dimensional optimal stopping problem and solving the equivalent free-boundary problem by means of the smooth-fit conditions.application/pdfeng510Report