  This work considers the problem of quickest detection with N distributed
sensors that receive continuous sequential observations from the environment.
These sensors employ cumulative sum (CUSUM) strategies and communicate to a
central fusion center by one shot schemes. One shot schemes are schemes in
which the sensors communicate with the fusion center only once, after which
they must signal a detection. The communication is clearly asynchronous and the
case is considered in which the fusion center employs a minimal strategy, which
means that it declares an alarm when the first communication takes place. It is
assumed that the observations received at the sensors are independent and that
the time points at which the appearance of a signal can take place are
different. It is shown that there is no loss of performance of one shot schemes
as compared to the centralized case in an extended Lorden min-max sense, since
the minimum of N CUSUMs is asymptotically optimal as the mean time between
false alarms increases without bound.
