  This work considers the problem of quickest detection of signals in a coupled
system of N sensors, which receive continuous sequential observations from the
environment. It is assumed that the signals, which are modeled a general Ito
processes, are coupled across sensors, but that their onset times may differ
from sensor to sensor. The objective is the optimal detection of the first time
at which any sensor in the system receives a signal. The problem is formulated
as a stochastic optimization problem in which an extended average Kullback-
Leibler divergence criterion is used as a measure of detection delay, with a
constraint on the mean time between false alarms. The case in which the sensors
employ cumulative sum (CUSUM) strategies is considered, and it is proved that
the minimum of N CUSUMs is asymptotically optimal as the mean time between
false alarms increases without bound.
