An optimal procedure for testing hypotheses on cadlag processes

Abstract

We consider a process X whose paths are right-continuous and have limits from the left, and denote by P its law. If P0 and P1 are two given probability measures, we show that under some conditions, Wald's sequential procedure for testing H0 : P = P0 versus H1 : P = P1 is optimal among a certain class of decision rules, in the sense that it minimizes the Kullback informations under both probability measures. As a conclusion,we give some applications of this result.