Loss and recovery of information by coarse observation of stochastic chain

Abstract

In a stationary stochastic chain, the states are grouped into classes or coarsely defined macrostates, engendering another chain defined in terms of macrostates. Comparison of information content of these two chains is made in detail. Loss of information caused by the coarseness of the definition of macrostates can be recovered, partially or totally depending on the case, when there is correlation in the chain. The range of correlation in some cases is increased by the coarse definition of states, thus creating a longer "aftereffect." If the correlation is weak, this aftereffect tapers off exponentially with time. © 1961 Academic Press Inc.