Mathematical Notes

, Volume 90, Issue 5–6, pp 920–924 | Cite as

A generalization of the Curtiss theorem for moment generating functions

Article

Abstract

The Curtiss theorem deals with the relation between the weak convergence of probability measures on the line and the convergence of theirmoment generating functions in a neighborhood of zero. We present a multidimensional generalization of this result. To this end, we consider arbitrary σ-finite measures whose moment generating functions exist in a domain of multidimensional Euclidean space not necessarily containing zero. We also prove the corresponding converse statement.

Keywords

probability measure moment generating function Curtiss theorem σ-finite measure analytic function Radon-Nykodym derivative 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesSteklovRussia

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