Asymptotic Near-Minimaxity of the Randomized Shiryaev-Roberts-Pollak Change-Point Detection Procedure in Continuous Time

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 1985) 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 et al. (2009) for the very same problem.