A generalization of the Curtiss theorem for moment generating functions (Q2435886)
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| Language | Label | Description | Also known as |
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| English | A generalization of the Curtiss theorem for moment generating functions |
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A generalization of the Curtiss theorem for moment generating functions (English)
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20 February 2014
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The Curtiss theorem [\textit{J. H. Curtiss}, Ann. Math. Stat. 13, 430--433 (1942; Zbl 0063.01024)] deals with the relation between the weak convergence of probability measures on the real line and the convergence of their moment generating functions in a neighbourhood of zero. \textit{A. Mukherjea} et al. [Stat. Probab. Lett. 76, No. 11, 1185--1189 (2006; Zbl 1092.60008)] extended this theorem to the case in which the interval for the existence of moment generating functions does not contain zero point. The author generalizes these results in two directions: to the multidimensional case and to arbitrary \(\sigma\)-finite mesures. In addition, the author presents the corresponding converse statement.
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probability measure
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moment generating function
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Curtiss theorem
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\(\sigma\)-finite measure
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analytic function
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Radon-Nykodym derivative
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