We study the behavior of mixture stopping rules in the one-sided sequential
hypothesis testing problem with a simple null hypothesis and a composite
alternative hypothesis. When the alternative hypothesis consists of a finite
set of probability measures, we show how to select a particular mixing
distribution in order to obtain a nearly minimax mixture test in the sense of
minimizing the maximal Kullback-Leibler information.

The problem of decentralized parameter estimation is considered for
diffusion-type processes whose drift coefficients are linear with respect to
the unknown parameter. This problem is motivated by applications where remote
sensors observe coupled stochastic processes and transmit quantized versions of
their data to a fusion center, for the latter to take the final decision. Novel
decentralized estimation schemes are suggested, according to which the sensors
communicate at two-sided exit times of appropriate sufficient statistics.