Geodesic
A Generalization of the Curtiss Theorem for Moment Generating Functions
Matematičeskie zametki, Tome 90 (2011) no. 6, pp. 947-952.

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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. 
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A. L. Yakymiv. A Generalization of the Curtiss Theorem for Moment Generating Functions. Matematičeskie zametki, Tome 90 (2011) no. 6, pp. 947-952. http://geodesic.mathdoc.fr/item/MZM_2011_90_6_a9/

[1] J. H. Curtiss, “A note on the theory of moment generating functions”, Ann. Math. Statist., 13:4 (1942), 430–433 | DOI | MR | Zbl

[2] V. N. Sachkov, Veroyatnostnye metody v kombinatornom analize, Nauka, M., 1978 | MR | Zbl

[3] V. N. Sachkov, Vvedenie v kombinatornye metody diskretnoi matematiki, MTsNMO, M., 2004

[4] A. L. Yakymiv, Veroyatnostnye prilozheniya tauberovykh teorem, Fizmatlit, M., 2005 | MR | Zbl

[5] A. Mukherjea, M. Rao, S. Suen, “A note on moment generating functions”, Statist. Probab. Lett., 76:11 (2006), 1185–1189 | DOI | MR | Zbl

[6] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1984 | MR | Zbl

[7] A. L. Yakymiv, “Predelnaya teorema dlya logarifma poryadka sluchainoi $A$-podstanovki”, Diskret. matem., 22:1 (2010), 126–149 | MR | Zbl

[8] Varadarain, “Mery na topologicheskikh prostranstvakh”, Matem. sb., 55:1 (1961), 35–100 | MR | Zbl

[9] V. S. Vladimirov, Metody teorii funktsii mnogikh kompleksnykh peremennykh, Nauka, M., 1964 | MR | Zbl

[10] B. V. Shabat, Vvedenie v kompleksnyi analiz. Ch. 2: Funktsii neskolkikh peremennykh, Nauka, M., 1976 | MR | Zbl