Tracking Stopping Times Through Noisy Observations

A novel quickest detection setting is proposed, generalizing the well-known Bayesian change-point detection model. Suppose
{(Xi
,
Yi
)}
i
ges 1 is a sequence of pairs of random variables, and that
S
is a stopping time with respect to
{Xi
}
i
ges 1. The problem is to find a stopping time
T
with respect to
{Yi
}
i
ges 1 that optimally tracks
S
, in the sense that
T
minimizes the expected
reaction

delay

\BBE

(T
-
S
)
⁺
, while keeping the
false-alarm

probability
P(Talpha

isin

[0,1]
. This problem formulation applies in several areas, such as in communication, detection, forecasting, and quality control.