A relationship between the growth-rate of logoptimal portfolios and capacity of fading single-input multiple output (SIMO) channels are established. Using this relation, stock vector stochastic processes that model the investment environments are stochastically ordered using different criteria. The presence of side information (SI) is considered, and a bound on the gains in the growth-rate due to SI is derived along with data processing inequality and convexity properties. A statistical test on the usefulness of SI that does not require the computation of the optimal portfolio vector in the presence of SI is introduced and its several variants are discussed.

中文翻译：

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衰落通道的投资组合增长率和遍历容量

建立了最简组合的增长率与衰落的单输入多输出（SIMO）通道的容量之间的关系。使用这种关系，可以使用不同的标准随机地对模拟投资环境的股票向量随机过程进行排序。考虑到辅助信息（SI）的存在，并伴随数据处理的不等式和凸度特性推导了由于SI导致的增长率提高的界限。介绍了一种关于SI有用性的统计测试，该统计测试不需要在存在SI的情况下计算最优投资组合向量，并且讨论了它的几种变体。