Continuous sequential decision in the presence of a finite number of hypotheses

Given a finite probability space
X
and an a priori distribution
P = P(0) = \{p_{i}(0)\}
, exact expressions for minimum search time (to determine the one and only one nonzero mean process) are derived. Only one point
i
may be observed at a given time, in contrast to the more standard decision theory problem where all n processes are observed simultaneously. The problem is formulated in continuous time, as a limiting case of discrete-time hypothesis tests. The performance of the optimal strategy is shown to be far superior to the performance of some standard strategies.