Equation of self-parallel curve deviation on statistical manifolds. (English) Zbl 0933.62100
The authors derive a differential equation for a self-parallel curve deviation on a statistical manifold [for the latter see S.-I. Amari, Differential-geometrical methods in statistics. (1985; Zbl 0559.62001)]. It is assumed that the self-parallel curves are neighbouring both in position and velocity, and also with respect to a one-parameter family of linear connections. The cases of the Gaussian manifold and the manifold of multinomial distributions are considered in detail.
Reviewer: A.N.Kochubei (Kyïv)
MSC:
62M99 | Inference from stochastic processes |
60D05 | Geometric probability and stochastic geometry |
53C99 | Global differential geometry |