Statistical structures on metric path spaces

Abstract

The authors extend the notion of statistical structure from Riemannian geometry to the general framework of path spaces endowed with a nonlinear connection and a generalized metric. Two particular cases of statistical data are defined. The existence and uniqueness of a nonlinear connection corresponding to these classes is proved. Two Koszul tensors are introduced in accordance with the Riemannian approach. As applications, the authors treat the Finslerian (α, β)-metrics and the Beil metrics used in relativity and field theories while the support Riemannian metric is the Fisher-Rao metric of a statistical model.

Keywords

Semispray / Nonlinear connection / Metric path space / Statistical structure / Skewness / Koszul tensors / (α, β)-metric / Beil metric / Rayleigh statistical structure / Fisher-Rao metric / Statistical model

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