On the dimension reduction in the quickest detection problem for diffusion processes with exponential penalty for the delay (Q2078229)

The author considers the problem of quickest detection of a change in the drift rate of an observable time-homogeneous diffusion process under the assumption that the detection delay is exponentially penalized. According to the existing literature, such problems are normally embedded into the corresponding optimal stopping problems for two-dimensional or three-dimensional Markov processes. In the paper under review, the author shows how a change of measure may significantly simplify the setting by means of reducing the appropriate dimension of the optimal stopping problem to one or two, respectively. The results are illustrated on the well-known cases of the observable Brownian motion analyzed by \textit{M. Beibel} [Ann. Stat. 28, No. 6, 1696--1701 (2000; Zbl 1105.62366)] and the observable Bessel process analyzed by \textit{P. Johnson} and \textit{G. Peskir} [Ann. Appl. Probab. 27, No. 2, 1003--1056 (2017; Zbl 1370.60135)] for the case of linear detection delay penalty.