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--- seminars:stat:141009 [2014/10/04 14:24] – qyu
+++ seminars:stat:141009 [2014/10/04 14:30] (current) – qyu
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+<WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP>
+~~META:title =October 9, 2014~~
+<WRAP 70% center>
+|  **DATE:**|Thursday, October 9, 2014 |
+|  **TIME:**|1:15pm to 2:15pm |
+|  **PLACE:**|OW 100E |
+|  **SPEAKER:**|Grigory Sokolov (Binghamton University) |
+|  **TITLE:**|On the Pre-Change Transition Probability Density of the Generalized Shiryaev--Roberts Change-Point Detection Procedure's Statistic in the Minimax Brownian Motion Setup|
+</WRAP>
+\\
+<WRAP center box 80%>
+<WRAP centeralign>**Abstract**</WRAP>
+We consider the problem of quickest change-point detection in continuous
+time where the observed is a standard Brownian motion that may, at an
+unknown moment in time, gain a persistent drift of a specified magnitude,
+and the objective is to as quickly and as reliably as possible detect the
+onset of the drift. Within this context, the specific focus is on the
+emerging Generalized Shiryaev-Roberts (GSR) detection procedure. We derive
+a closed-form formula for the pre-change transition probability density of
+the diffusion process associated with the GSR decision statistic; the
+transition probability density formula is found through direct solution of
+the respective Kolmogorov forward equation (otherwise also known as the
+Fokker--Planck equation, and closely connected to the Smoluchowski equation
+and the Schrödinger equation from physics) via the Fourier spectral method.
+To conclude, we exploit the obtained formulae numerically and offer a brief
+study of the GSR statistic's behavior in the pre-change regime.
+This work (and in particular the methodology employed in it) may help gain
+greater insight into the characteristics of the GSR procedure in continuous
+time and thus foster and facilitate further research on both theoretical
+and applied change-point detection.
+This is joint work with Aleksey Polunchenko (SUNY Binghamton).
+</WRAP>