155 citations · 486 across the 22 of their papers we have counts for
27 papers
More On the Quasi-Stationary Distribution of the Shiryaev--Roberts Diffusion
Soumik Banerjee, Aleksey S. Polunchenko
We consider the classical Shiryaev--Roberts martingale diffusion, , restricted to the interval , where is a preset absorbing boundary. We take yet anoth…
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…
Optimal Design of the Shiryaev-Roberts Chart: Give Your Shiryaev-Roberts a Headstart
Aleksey S. Polunchenko
We offer a numerical study of the effect of headstarting on the performance of a Shiryaev-Roberts (SR) chart set up to control the mean of a normal process. The study is a natural…
Asymptotic Near-Minimaxity of the Randomized Shiryaev-Roberts-Pollak Change-Point Detection Procedure in Continuous Time
Aleksey S. Polunchenko
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…
On the Quasi-Stationary Distribution of the Shiryaev-Roberts Diffusion
Aleksey S. Polunchenko
We consider the diffusion generated by the equation with fixed, and where is given, and i…
A Note on Efficient Performance Evaluation of the Cumulative Sum Chart and the Sequential Probability Ratio Test
Aleksey S. Polunchenko
We establish a simple connection between certain in-control characteristics of the CUSUM Run Length and their out-of-control counterparts. The connection is in the form of paired i…
An Analytic Expression for the Distribution of the Generalized Shiryaev-Roberts Diffusion
Aleksey S. Polunchenko, Grigory Sokolov
We consider the quickest change-point detection problem where the aim is to detect the onset of a pre-specified drift in "live"-monitored standard Brownian motion; the change-point…
Exact Distribution of the Generalized Shiryaev-Roberts Stopping Time Under the Minimax Brownian Motion Setup
Aleksey S. Polunchenko
We consider the quickest change-point detection problem where the aim is to detect the onset of a pre-specified drift in "live"-monitored standard Brownian motion; the change-point…
Real-time financial surveillance via quickest change-point detection methods
Andrey Pepelyshev, Aleksey S. Polunchenko
We consider the problem of efficient financial surveillance aimed at "on-the-go" detection of structural breaks (anomalies) in "live"-monitored financial time series. With the prob…
On Robustness of the Shiryaev-Roberts Procedure for Quickest Change-Point Detection under Parameter Misspecification in the Post-Change Distribution
Wenyu Du, Aleksey S. Polunchenko, Grigory Sokolov
The gist of the quickest change-point detection problem is to detect the presence of a change in the statistical behavior of a series of sequentially made observations, and do so i…
An Exact Formula for the Average Run Length to False Alarm of the Generalized Shiryaev-Roberts Procedure for Change-Point Detection under Exponential Observations
Wenyu Du, Grigory Sokolov, Aleksey S. Polunchenko
We derive analytically an exact closed-form formula for the standard minimax Average Run Length (ARL) to false alarm delivered by the Generalized Shiryaev-Roberts (GSR) change-poin…
Efficient Performance Evaluation of the Generalized Shiryaev--Roberts Detection Procedure in a Multi-Cyclic Setup
Aleksey S. Polunchenko, Grigory Sokolov, Wenyu Du
We propose a numerical method to evaluate the performance of the emerging Generalized Shiryaev--Roberts (GSR) change-point detection procedure in a "minimax-ish" multi-cyclic setup…
Quickest Change-Point Detection: A Bird's Eye View
Aleksey S. Polunchenko, Grigory Sokolov, Wenyu Du
We provide a bird's eye view onto the area of sequential change-point detection. We focus on the discrete-time case with known pre- and post-change data distributions and offer a s…
Optimal Design and Analysis of the Exponentially Weighted Moving Average Chart for Exponential Data
Aleksey S. Polunchenko, Grigory Sokolov, Alexander G. Tartakovsky
We study optimal design of the Exponentially Weighted Moving Average (EWMA) chart by a proper choice of the smoothing factor and the initial value (headstart) of the decision stati…
An Accurate Method for Determining the Pre-Change Run-Length Distribution of the Generalized Shiryaev--Roberts Detection Procedure
Aleksey S. Polunchenko, Grigory Sokolov, Wenyu Du
Change-of-measure is a powerful technique used across statistics, probability and analysis. Particularly known as Wald's likelihood ratio identity, the technique enabled the proof…
Efficient Computer Network Anomaly Detection by Changepoint Detection Methods
Alexander G. Tartakovsky, Aleksey S. Polunchenko, Grigory Sokolov
We consider the problem of efficient on-line anomaly detection in computer network traffic. The problem is approached statistically, as that of sequential (quickest) changepoint de…
Nearly Optimal Change-Point Detection with an Application to Cybersecurity
Aleksey S. Polunchenko, Alexander G. Tartakovsky, Nitis Mukhopadhyay
We address the sequential change-point detection problem for the Gaussian model where baseline distribution is Gaussian with variance σ^2 and mean μsuch that σ^2=aμ, where a>0 is a…
State-of-the-Art in Sequential Change-Point Detection
Aleksey S. Polunchenko, Alexander G. Tartakovsky
We provide an overview of the state-of-the-art in the area of sequential change-point detection assuming discrete time and known pre- and post-change distributions. The overview sp…
Third-order Asymptotic Optimality of the Generalized Shiryaev-Roberts Changepoint Detection Procedures
Alexander G. Tartakovsky, Moshe Pollak, Aleksey S. Polunchenko
Several variations of the Shiryaev-Roberts detection procedure in the context of the simple changepoint problem are considered: starting the procedure at (the original Shir…