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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 .
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].
Amine Asselah (2010)
Annales de l'I.H.P. Probabilités et statistiques
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We reveal a shape transition for a transient simple random walk forced to realize an excess -norm of the local times, as the parameter crosses the value ()=/(−2). Also, as an application of our approach, we establish a central limit theorem for the -norm of the local times in dimension 4 or more.
P. Ney, S. Wainger (1972)
Studia Mathematica
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Michael B. Marcus, Jay Rosen (1997)
Annales de l'I.H.P. Probabilités et statistiques
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Carsten Schütt (1984)
Studia Mathematica
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Matthias Birkner, Rongfeng Sun (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We study the continuous time version of the , where conditioned on a continuous time random walk ( )≥0 on ℤ with jump rate > 0, which plays the role of disorder, the law up to time of a second independent random walk ( )0≤≤ with jump rate 1 is Gibbs transformed with weight e (,), where (, ) is the collision local time between and up to time . As the inverse temperature varies, the model undergoes a localization–delocalization...