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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.

Received: 06.03.1993

Language: English

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

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