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A characterization of some probability distributions

  • Nguyen Van Thu
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 828)

Abstract

The aim of the present paper is to give a characterization of a probability distribution μn+1 (n=1, 2, ...) on a real separable Banach space (X, ‖ · ‖) such that for some probability distributions μ1, ..., μn and c1, ..., cn ε (0,1) the following convolution equations hold:
$$\mu _k = T_{c_k } \mu _k *\mu _{k + 1} (k = 1,2,...,n) .$$
(1)

Keywords

Probability Distribution Banach Space Integer Part Orlicz Space Nondecreasing Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    K. Ito, M. Nisio, On the convergence of sums of independent Banach space valued random variables, Osaka Journal of Math. 5 (1968) pp.35–48.MathSciNetzbMATHGoogle Scholar
  2. [2]
    O.K. Zakusilo, On classes of limit distributions in some scheme of summing up (in Russian), Probability Theory and Mathematical Statistics, vol.12, Kiev 1975.Google Scholar
  3. [3]
    K. Urbanik, Lévy’s probability measures on Banach spaces, Studia Math. Tom LXIII, Fasc.3 (1978), pp.283–308.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Nguyen Van Thu
    • 1
  1. 1.Institute of MathematicsHanoiVietnam

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