Geodesic
A curious example from statistical differential geometry
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 1, pp. 116-140

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We consider an example of a family of probability measures on an infinite dimensional space which are mutually singular. Although the Fisher information metric and its variants are not available, it is shown that the parameter manifold has a natural differential structure that is non-Riemannian with nonzero curvature. It is also shown that there is no Riemannian metric compatible with the natural affine connection for which the curvature is not zero.
Keywords: stochastic partial differential equation, parameter manifold, affine connection, non-Riemannian geometry. 
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     author = {G. Kallianpur and Y.-T. Kim},
     title = {A curious example from statistical differential geometry},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {116--140},
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_1_a7/}
}
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G. Kallianpur; Y.-T. Kim. A curious example from statistical differential geometry. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 1, pp. 116-140. http://geodesic.mathdoc.fr/item/TVP_1998_43_1_a7/