October 9, 2014 [Department of Mathematics and Statistics, Binghamton University]

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<WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP>

~~META:title =October 9, 2014~~
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|  **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|
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<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).

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