  We consider a quantum system that is being continuously monitored, giving
rise to a measurement signal. From such a stream of data, information needs to
be inferred about the underlying system's dynamics. Here we focus on hypothesis
testing problems and put forward the usage of sequential strategies where the
signal is analyzed in real time, allowing the experiment to be concluded as
soon as the underlying hypothesis can be identified with a certified prescribed
success probability. We analyze the performance of sequential tests by studying
the stopping-time behavior, showing a considerable advantage over
currently-used strategies based on a fixed predetermined measurement time.
