Gaussian chaos and functional laws of the iterated logarithm for Ito-Wiener integrals
V. Goodman, J. Kuelbs (1993)
Annales de l'I.H.P. Probabilités et statistiques
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V. Goodman, J. Kuelbs (1993)
Annales de l'I.H.P. Probabilités et statistiques
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Elena Kosygina, Thomas Mountford (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We consider excited random walks (ERWs) on ℤ with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [15] have shown that when the total expected drift per site, , is larger than 1 then ERW is transient to the right and, moreover, for >4 under the averaged measure it obeys the Central Limit Theorem. We show that when ∈(2, 4] the limiting behavior of an appropriately centered and scaled excited...
Arnaud Gloter, Emmanuel Gobet (2008)
Annales de l'I.H.P. Probabilités et statistiques
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In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process . Our data are given by d() for =0, …, −1 and the unknown parameter appears in the diffusion coefficient of the process only. Although the data are neither markovian nor gaussian we can write down, with help of Malliavin calculus, an explicit expression for...
J. A. Cuesta-Albertos, C. Matrán (1998)
Annales de l'I.H.P. Probabilités et statistiques
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A. J. Stam (1971)
Compositio Mathematica
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David Márquez-Carreras, Marta Sanz-Solé (1998)
Collectanea Mathematica
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