Statistical Structures on Metric Path Spaces

The authors extend the notion of statistical structure from Riemannian geom- etry 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 corresp...

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Veröffentlicht in:	Chinese annals of mathematics. Serie B 2012-11, Vol.33 (6), p.889-902
1. Verfasser:	Mircea CRASMAREANU Cristina-Elena HRETCANU
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Koszul模 Mathematics Mathematics and Statistics 公制广义度量空间空间结构统计数据统计结构路径黎曼度量
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creator	Mircea CRASMAREANU Cristina-Elena HRETCANU
description	The authors extend the notion of statistical structure from Riemannian geom- etry 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.
doi_str_mv	10.1007/s11401-012-0745-9
format	Article
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subjects	Applications of Mathematics Koszul模 Mathematics Mathematics and Statistics 公制广义度量空间空间结构统计数据统计结构路径黎曼度量
title	Statistical Structures on Metric Path Spaces
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