Extended Divergence on a Foliation by Deformed Probability Simplexes.

This study considers a new decomposition of an extended divergence on a foliation by deformed probability simplexes from the information geometry perspective. In particular, we treat the case where each deformed probability simplex corresponds to a set of -escort distributions. For the foliation, different -parameters and the corresponding α-parameters of dualistic structures are defined on each of the various leaves. We propose the divergence decomposition theorem that guides the proximity of -escort distributions with different -parameters and compare the new theorem to the previous theorem of the standard divergence on a Hessian manifold with a fixed α-parameter.