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Teor. Veroyatnost. i Primenen., 1995, Volume 40, Issue 4, Pages 929–934 (Mi tvp3742)  

Short Communications

A generalization of Е. Siebert's theorem on convergence of convolution semigroups and accompanying laws

W. Hazod

Institut für Mathematik, Universität Dortmund, Dortmund, Germany

Abstract: The convergence of sequences of convolution semigroups of probabilities in terms of their generating functionals is described. The equivalence of the convergence of the accompanying laws and the corresponding generating functionals is proved in the case of an arbitrary locally compact group.

Keywords: continuous and discrete convolution semigroups, generating functionals, accompanying laws, convergence of convolution semigroups, domains of attraction.

Full text: PDF file (406 kB)

English version:
Theory of Probability and its Applications, 1995, 40:4, 765–769

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Received: 06.03.1993
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Citation: W. Hazod, “A generalization of Е. Siebert's theorem on convergence of convolution semigroups and accompanying laws”, Teor. Veroyatnost. i Primenen., 40:4 (1995), 929–934; Theory Probab. Appl., 40:4 (1995), 765–769

Citation in format AMSBIB
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\by W.~Hazod
\paper A generalization of Е.~Siebert's theorem on convergence of convolution semigroups and accompanying laws
\jour Teor. Veroyatnost. i Primenen.
\yr 1995
\vol 40
\issue 4
\pages 929--934
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1405162}
\zmath{https://zbmath.org/?q=an:0857.60007}
\transl
\jour Theory Probab. Appl.
\yr 1995
\vol 40
\issue 4
\pages 765--769
\crossref{https://doi.org/10.1137/1140088}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WD22100018}


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