Geodesic
Asymptotic near-minimaxity of the randomized Shiryaev--Roberts--Pollak change-point detection procedure in continuous time
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 769-786

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For the classical continuous-time quickest change-point detection problem it is shown that the randomized Shiryaev–Roberts–Pollak procedure is asymptotically nearly minimax-optimal (in the sense of Pollak [Ann. Statist., 13 (1985), pp. 206–227]) in the class of randomized procedures with vanishingly small false alarm risk. The proof is explicit in that all of the relevant performance characteristics are found analytically and in a closed form. The rate of convergence to the (unknown) optimum is elucidated as well. The obtained optimality result is a one-order improvement of that previously obtained by Burnaev, Feinberg, and Shiryaev [Theory Probab. Appl., 53 (2009), pp. 519–536] for the very same problem.
Keywords: minimax optimality, optimal stopping, quasi-stationary distribution, sequential change-point detection, Shiryaev–Roberts procedure. 
@article{TVP_2017_62_4_a6,
     author = {A. S. Polunchenko},
     title = {Asymptotic near-minimaxity of the randomized {Shiryaev--Roberts--Pollak} change-point detection procedure in continuous time},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {769--786},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a6/}
}
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A. S. Polunchenko. Asymptotic near-minimaxity of the randomized Shiryaev--Roberts--Pollak change-point detection procedure in continuous time. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 769-786. http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a6/