Stable convergence of generalized stochastic integrals and the principle of conditioning.
Giovanni, Peccati, Taqqu, Murad S. (2007)
Electronic Journal of Probability [electronic only]
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Giovanni, Peccati, Taqqu, Murad S. (2007)
Electronic Journal of Probability [electronic only]
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Gregory J. Morrow, Martin L. Silverstein (1986)
Séminaire de probabilités de Strasbourg
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Gnedin, Alexander, Olshanski, Grigori (2009)
The Electronic Journal of Combinatorics [electronic only]
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Evarist Giné, José R. León (1980)
Stochastica
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The object of this paper is to prove a central limit theorem in (separable) Hilbert space using a method based on the so called découpage de Lévy, the Lindeberg proof for the Gaussian case and an elementary proof of Poisson convergence for the direct part, and on elementary probabilistic inequalities for the converse. In particular, characteristic functions are only used in unicity questions. Several results of Varadhan (1962) can be obtained either directly as corollaries of the main...
František Straka, Josef Štěpán (1993)
Mathematica Slovaca
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Arcones, Miguel A. (1999)
Electronic Journal of Probability [electronic only]
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Zemlys, Vaidotas (2008)
Electronic Journal of Probability [electronic only]
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Vidyadhar Mandrekar (1983)
Séminaire de probabilités de Strasbourg
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Walter Schachermayer (1999)
Séminaire de probabilités de Strasbourg
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Mohamedou Ould Haye (2002)
ESAIM: Probability and Statistics
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We study the asymptotic behavior of the empirical process when the underlying data are gaussian and exhibit seasonal long-memory. We prove that the limiting process can be quite different from the limit obtained in the case of regular long-memory. However, in both cases, the limiting process is degenerated. We apply our results to von–Mises functionals and -Statistics.