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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.

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

Bibliographic databases:

UDC: 519.2
Received: 22.04.1968

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
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\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}


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