Information Geometry for Random Walk

The random walk (RW) is investigated from the viewpoint of information geometry and shown to be an exponential family distribution. It has a dual coordinate system and a dual geometric structure. Then submanifolds of RW manifold is studied, and the e-flat hierarchical structure and the orthogonal foliations of RW manifold are obtained. Finally, using the Kullback-Leibler divergence, the projections are given from the RW manifold to its submanifolds.