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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1970, Volume 7, Issue 6, Pages 707–715 (Mi mz9556)

Invariant finite-dimensional exponential families on homogeneous spaces

P. N. Sapozhnikov

A. M. Gor'ki Perm State University

Abstract: A general form is obtained for the finite-dimensional exponential family invariant with respect to a locally compact group $G$ when it is defined on the measurable quotient spade $(G/\Gamma, \mathcal{A}, \mu)$ of this group with respect to a subgroup $\Gamma$. Conditions for the existence of such families are derived. Examples are given of exponential families on a compact homogeneous space, and the general form of families in $R_n$ invariant with respect to $GL(n)$ is obtained.

Full text: PDF file (1008 kB)

English version:
Mathematical Notes, 1970, 7:6, 427–431

Bibliographic databases:

UDC: 519.2

Citation: P. N. Sapozhnikov, “Invariant finite-dimensional exponential families on homogeneous spaces”, Mat. Zametki, 7:6 (1970), 707–715; Math. Notes, 7:6 (1970), 427–431

Citation in format AMSBIB
\Bibitem{Sap70} \by P.~N.~Sapozhnikov \paper Invariant finite-dimensional exponential families on homogeneous spaces \jour Mat. Zametki \yr 1970 \vol 7 \issue 6 \pages 707--715 \mathnet{http://mi.mathnet.ru/mz9556} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=264728} \zmath{https://zbmath.org/?q=an:0214.28802|0211.34902} \transl \jour Math. Notes \yr 1970 \vol 7 \issue 6 \pages 427--431 \crossref{https://doi.org/10.1007/BF01093600}