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Teor. Veroyatnost. i Primenen., 1975, Volume 20, Issue 3, Pages 661–664 (Mi tvp3327)  

Short Communications

On the factorization of infinitely divisible distributions

A. E. Fryntov

Physical Engineering Institute of Low Temperatures, UkrSSR Academy of Sciences

Abstract: The article deals with the necessary and sufficient condition under which the infinitely divisible law $F$ having the finite spectral Levy's measure $\mu$ which is concentrated on the set of positive rational numbers and
$$ \mu([y,\infty))=O\{\exp(-Ky^2)\},\quad y\to+\infty,\quad\exists K>0, $$
belongs to $I_0$. The following result is also established: if $F\in I_0$ and $(\alpha\in(0,1))$
$$ \varliminf_{r\to0}\ln\mu([\alpha r,r])/\ln(1/|r|)>1, $$
then $F$ belongs to Linnik's class $\mathfrak E$.

Full text: PDF file (292 kB)

English version:
Theory of Probability and its Applications, 1976, 20:3, 644–648

Bibliographic databases:

Received: 20.03.1975

Citation: A. E. Fryntov, “On the factorization of infinitely divisible distributions”, Teor. Veroyatnost. i Primenen., 20:3 (1975), 661–664; Theory Probab. Appl., 20:3 (1976), 644–648

Citation in format AMSBIB
\Bibitem{Fry75}
\by A.~E.~Fryntov
\paper On the factorization of infinitely divisible distributions
\jour Teor. Veroyatnost. i Primenen.
\yr 1975
\vol 20
\issue 3
\pages 661--664
\mathnet{http://mi.mathnet.ru/tvp3327}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=378026}
\zmath{https://zbmath.org/?q=an:0351.60026}
\transl
\jour Theory Probab. Appl.
\yr 1976
\vol 20
\issue 3
\pages 644--648
\crossref{https://doi.org/10.1137/1120073}


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