Some dynamical properties of sequentially acquired information (abstract only)0

Abstract

In this paper we obtain two closely related theorems that essentially say that no matter what information metric is used, on the average the value of the accumulated information at stopping time is bounded by a multiple of the expected stopping time. These results are also independent of the particular stopping strategy employed although they do require that the expected stopping time be finite. These results, along with a general type of stopping strategy based on incremental information, are given. Later we apply our general theorem to a specific stopping strategy associated with the GIS model. Although we concentrate on the problem of stopping, the information function on which this stopping decision is based can also be used to choose the COA for the next cycle of the feedback loop. We apply our results to an estimation problem involving the well known Shannon-Weiner measure of information. Since our theorems require that the expected stopping times be finite, sometime is devoted to a discussion of necessary and sufficient conditions for finite expected stopping times.