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Short Communications
Об абсолютной непрерывности безгранично делимых распределений при сдвигах
A. V. Skorokhod Kiev
Abstract:
Random variables $\xi$ with values in a separable Hilbert space $H$ with infinitely divisible distributions are considered. Some sufficient conditions for the absolute continuity of the measure corresponding to $\xi+a$ ($a\in H$) with respect to the measure corresponding to $\xi$ are obtained.
Let now $H$ denote the real line and let the characteristic function of $\xi$ be
$$
\exp\{\int(e^{ixt}-1-\frac{ixt}{1+x^2})\Pi(dx)\}.
$$
It is proved that in this case $\xi$ has a density when the condition $\int_{-1}^1|x|\Pi(dx)=\infty$ is satisfied.
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Theory of Probability and its Applications, 1965, 10:3, 465–472
Bibliographic databases:
Received: 14.01.1965
Citation:
A. V. Skorokhod, “Об абсолютной непрерывности безгранично делимых распределений при сдвигах”, Teor. Veroyatnost. i Primenen., 10:3 (1965), 510–518; Theory Probab. Appl., 10:3 (1965), 465–472
Citation in format AMSBIB
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\by A.~V.~Skorokhod
\paper Об абсолютной непрерывности безгранично делимых распределений при сдвигах
\jour Teor. Veroyatnost. i Primenen.
\yr 1965
\vol 10
\issue 3
\pages 510--518
\mathnet{http://mi.mathnet.ru/tvp546}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=189125}
\zmath{https://zbmath.org/?q=an:0203.19803}
\transl
\jour Theory Probab. Appl.
\yr 1965
\vol 10
\issue 3
\pages 465--472
\crossref{https://doi.org/10.1137/1110054}
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http://mi.mathnet.ru/eng/tvp546 http://mi.mathnet.ru/eng/tvp/v10/i3/p510
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