Some results on the continuity of stable processes and the domain of attraction of continuous stable processes
M. B. Marcus, G. Pisier (1984)
Annales de l'I.H.P. Probabilités et statistiques
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M. B. Marcus, G. Pisier (1984)
Annales de l'I.H.P. Probabilités et statistiques
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H. Kesten, M. V. Kozlov, F. Spitzer (1975)
Compositio Mathematica
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Franciszek Czekała (1996)
Applicationes Mathematicae
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The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].
M. Fisz (1954)
Studia Mathematica
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N. Guillotin (2000)
Annales de l'I.H.P. Probabilités et statistiques
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Klebanov, Lev, Rachev, Svetlozar (1996)
Serdica Mathematical Journal
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* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists. In this paper a general theory of a random number of random variables is constructed. A description of all random variables ν admitting an analog of the Gaussian distribution under ν-summation, that is, the summation of a random number ν of random terms, is given. The v-infinitely divisible distributions are described for these ν-summations and finite estimates of the approximation of ν-sum...
Richard Bass, Xia Chen, Jay Rosen (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We study functionals of the form = ⋯ | ( )+⋯+ ( )| d ⋯ d , where (), …, () are i.i.d. -dimensional symmetric stable processes of index 0<≤2. We obtain results about the large deviations and laws of the iterated logarithm for .