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A Ciesielski–Taylor type identity for positive self-similar Markov processes

A. E. Kyprianou, P. Patie (2011)

Annales de l'I.H.P. Probabilités et statistiques

The aim of this note is to give a straightforward proof of a general version of the Ciesielski–Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski–Taylor identities within the latter class. The approach makes use of three fundamental features. Firstly, a new transformation which maps a subset of the family of Laplace exponents of spectrally negative Lévy processes into itself. Secondly, some classical features...

A uniform dimension result for two-dimensional fractional multiplicative processes

Xiong Jin (2014)

Annales de l'I.H.P. Probabilités et statistiques

Given a two-dimensional fractional multiplicative process ( F t ) t ∈ [ 0 , 1 ] determined by two Hurst exponents H 1 and H 2 , we show that there is an associated uniform Hausdorff dimension result for the images of subsets of [ 0 , 1 ] by F if and only if H 1 = H 2 .

Asymptotic behavior of the empirical process for gaussian data presenting seasonal long-memory

Mohamedou Ould Haye (2002)

ESAIM: Probability and Statistics

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 U -Statistics.

Asymptotic behavior of the Empirical Process for Gaussian data presenting seasonal long-memory

Mohamedou Ould Haye (2010)

ESAIM: Probability and Statistics

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 U-Statistics.

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