Before revision:  The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992). We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races.
After revision:  The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races.