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Mat. Zametki, 2011, Volume 90, Issue 6, Pages 947–952 (Mi mz8535)  

This article is cited in 2 scientific papers (total in 2 papers)

A Generalization of the Curtiss Theorem for Moment Generating Functions

A. L. Yakymiv

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The Curtiss theorem deals with the relation between the weak convergence of probability measures on the line and the convergence of their moment generating functions in a neighborhood of zero. We present a multidimensional generalization of this result. To this end, we consider arbitrary $\sigma$-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, $\sigma$-finite measure, analytic function. Radon–Nykodym derivative

DOI: https://doi.org/10.4213/mzm8535

Full text: PDF file (412 kB)
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English version:
Mathematical Notes, 2011, 90:6, 920–924

Bibliographic databases:

Document Type: Article
UDC: 519.2
Received: 28.03.2011

Citation: A. L. Yakymiv, “A Generalization of the Curtiss Theorem for Moment Generating Functions”, Mat. Zametki, 90:6 (2011), 947–952; Math. Notes, 90:6 (2011), 920–924

Citation in format AMSBIB
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\paper A Generalization of the Curtiss Theorem for Moment Generating Functions
\jour Mat. Zametki
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\vol 90
\issue 6
\pages 947--952
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\crossref{https://doi.org/10.4213/mzm8535}
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\jour Math. Notes
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\issue 6
\pages 920--924
\crossref{https://doi.org/10.1134/S0001434611110290}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. L. Yakymiv, “Random $A$-permutations and Brownian motion”, Proc. Steklov Inst. Math., 282 (2013), 298–318  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
    2. Joutard C., “Multidimensional Strong Large Deviation Results”, Metrika, 80:6-8 (2017), 663–683  crossref  mathscinet  zmath  isi  scopus
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