A characterization of some probability distributions

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


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:
$$\mu _k = T_{c_k } \mu _k *\mu _{k + 1} (k = 1,2,...,n) .$$


Probability Distribution Banach Space Integer Part Orlicz Space Nondecreasing Function 
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    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
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    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
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    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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