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1996 | 118 | 2 | 185-204
Tytuł artykułu

A characterization of probability measures by f-moments

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EN
Abstrakty
EN
Given a real-valued continuous function ƒ on the half-line [0,∞) we denote by P*(ƒ) the set of all probability measures μ on [0,∞) with finite ƒ-moments $ʃ_{0}^{∞} ƒ(x)μ^{*n}(dx)$ (n = 1,2...). A function ƒ is said to have the identification property} if probability measures from P*(ƒ) are uniquely determined by their ƒ-moments. A function ƒ is said to be a Bernstein function} if it is infinitely differentiable on the open half-line (0,∞) and $(-1)^{n} ƒ^{(n+1)}(x)$ is completely monotone for some nonnegative integer n. The purpose of this paper is to give a necessary and sufficient condition in terms of the representing measures for Bernstein functions to have the identification property.
Czasopismo
Rocznik
Tom
118
Numer
2
Strony
185-204
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-10-09
poprawiono
1996-02-05
Twórcy
autor
Bibliografia
  • [1] M. Braverman, A characterization of probability distributions by moments of sums of independent random variables, J. Theoret. Probab. 7 (1994), 187-198.
  • [2] M. Braverman, C. L. Mallows and L. A. Shepp, A characterization of probability distributions by absolute moments of partial sums, Teor. Veroyatnost. i Primenen. 40 (1995), 270-285 (in Russian).
  • [3] W. Feller, On Müntz' theorem and completely monotone functions, Amer. Math. Monthly 75 (1968), 342-350.
  • [4] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, N.J., 1962.
  • [5] S. Kaczmarz und H. Steinhaus, Theorie der Orthogonalreihen, Monograf. Mat. 6, Warszawa-Lwów, 1935.
  • [6] L. H. Loomis, An Introduction to Abstract Harmonic Analysis, Van Nostrand, Toronto, 1953.
  • [7] C. Müntz, Über den Approximationssatz von Weierstrass, in: Schwarz Festschrift, Berlin, 1914, 303-312.
  • [8] M. Neupokoeva, On the reconstruction of distributions by the moments of the sums of independent random variables, in: Stability Problems for Stochastic Models, Proceedings, VNIISI, Moscow, 1989, 11-17 (in Russian).
  • [9] R. E. A. C. Paley and N. Wiener, Fourier Transforms in the Complex Domain, Amer. Math. Soc., New York, 1934.
  • [10] O. Szász, Über die Approximation stetiger Funktionen durch lineare Aggregate von Potenzen, Math. Ann. 77 (1916), 482-496.
  • [11] K. Urbanik, Moments of sums of independent random variables, in: Stochastic Processes (Kallianpur Festschrift), Springer, New York, 1993, 321-328.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv118i2p185bwm
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