Limit theorems for Banach-valued autoregressive processes. Applications to real continuous time processes.

Bosq, Denis

Displaying similar documents to “Limit theorems for Banach-valued autoregressive processes. Applications to real continuous time processes.”

Stationary solutions for integer-valued autoregressive processes.

Aly, Emad-Eldin A.A., Bouzar, Nadjib (2005)

International Journal of Mathematics and Mathematical Sciences

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Central limit theorem for Hölder processes on $ℝ^{m}$ -unit cube

Jana Klicnarová (2007)

Commentationes Mathematicae Universitatis Carolinae

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We consider a sequence of stochastic processes $(X_{n} (𝐭), 𝐭 \in {[0, 1]}^{m})$ with continuous trajectories and we show conditions for the tightness of the sequence in the Hölder space with a parameter $γ$ .

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

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 $U$ -Statistics.