9 papers
On the Convergence Rate of the Quasi- to Stationary Distribution for the Shiryaev-Roberts Diffusion
Kexuan Li, Aleksey S. Polunchenko
For the classical Shiryaev--Roberts martingale diffusion considered on the interval , where is a given absorbing boundary, it is shown that the rate of convergence of…
Analytic Evaluation of the Fractional Moments for the Quasi-Stationary Distribution of the Shiryaev Martingale on an Interval
Kexuan Li, Aleksey S. Polunchenko, Andrey Pepelyshev
We consider the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval with absorption at a fixed . We derive analytically a clos…
Analytic moment and Laplace transform formulae for the quasi-stationary distribution of the Shiryaev diffusion on an interval
Aleksey S. Polunchenko, Andrey Pepelyshev
We derive analytic closed-form moment and Laplace transform formulae for the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval wi…
A Note on the Quasi-Stationary Distribution of the Shiryaev Martingale on the Positive Half-Line
Aleksey S. Polunchenko, Servet Martinez, Jaime San Martin
We obtain a closed-form formula for the quasi-stationary distribution of the classical Shiryaev martingale diffusion considered on the positive half-line with f…
Comparative Performance Analysis of the Cumulative Sum Chart and the Shiryaev-Roberts Procedure for Detecting Changes in Autocorrelated Data
Aleksey S. Polunchenko, Vasanthan Raghavan
We consider the problem of quickest change-point detection where the observations form a first-order autoregressive (AR) process driven by temporally independent standard Gaussian…
Asymptotic Exponentiality of the First Exit Time of the Shiryaev-Roberts Diffusion with Constant Positive Drift
Aleksey S. Polunchenko
We consider the first exit time of a Shiryaev-Roberts diffusion with constant positive drift from the interval where . We show that the moment generating function (Lap…