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| Statistical Structures on Metric Path Spaces |
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Citation： |
Mircea CRASMAREANU,Cristina-Elena HRET¸CANU.Statistical Structures on Metric Path Spaces[J].Chinese Annals of Mathematics B,2012,33(6):889~902 |
| Page view： 1900
Net amount： 2466 |
Authors： |
Mircea CRASMAREANU; Cristina-Elena HRET?CANU; |
Foundation： |
the Romanian National Authority for Scientific Research, CNCS UEFISCDI (No.PN-II-ID-PCE-2012-4-0131). |
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| 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 |
Classification： |
53C05, 53C15, 53C60, 53B15, 53B20, 53C80 |
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