Geodesic
Filtered Arithmetic Mean Measure and Its Applications
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 2, pp. 354-364

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We consider fixed probability measures on a filtered space. We construct a new measure having the following property: the predictable characteristics of any semimartingale with respect to this measure are computed as the arithmetic mean of predictable characteristics with respect to initial probability measures. We present as an application of the measure a computable minimax risk estimation in Fano's lemma.
Keywords: triplet of predictable characteristics, Hellinger process, Kullback-Leibler process, Kullback–Leibler information, Fano's lemma. 
@article{TVP_2008_53_2_a9,
     author = {D. A. Zhdanov},
     title = {Filtered {Arithmetic} {Mean} {Measure} and {Its} {Applications}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {354--364},
     publisher = {mathdoc},
     volume = {53},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_2_a9/}
}
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D. A. Zhdanov. Filtered Arithmetic Mean Measure and Its Applications. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 2, pp. 354-364. http://geodesic.mathdoc.fr/item/TVP_2008_53_2_a9/