Displaying similar documents to “Bounds and asymptotic expansions for the distribution of the Maximum of a smooth stationary Gaussian process”

On the tails of the distribution of the maximum of a smooth stationary Gaussian process

Jean-Marc Azaïs, Jean-Marc Bardet, Mario Wschebor (2010)

ESAIM: Probability and Statistics

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We study the tails of the distribution of the maximum of a stationary Gaussian process on a bounded interval of the real line. Under regularity conditions including the existence of the spectral moment of order , we give an additional term for this asymptotics. This widens the application of an expansion given originally by Piterbarg [CITE] for a sufficiently small interval.

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

Mohamedou Ould Haye (2010)

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 long-memory. We prove that the limiting process can be quite different from the limit obtained in the case of long-memory. However, in both cases, the limiting process is degenerated. We apply our results to von–Mises functionals and -Statistics.

Asymptotic distribution of the estimated parameters of an ARMA(p,q) process in the presence of explosive roots

Sugata Sen Roy, Sankha Bhattacharya (2012)

Applicationes Mathematicae

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We consider an autoregressive moving average process of order (p,q)(ARMA(p,q)) with stationary, white noise error variables having uniformly bounded fourth order moments. The characteristic polynomials of both the autoregressive and moving average components involve stable and explosive roots. The autoregressive parameters are estimated by using the instrumental variable technique while the moving average parameters are estimated through a derived autoregressive process using the same...

On the tails of the distribution of the maximum of a smooth stationary gaussian process

Jean-Marc Azaïs, Jean-Marc Bardet, Mario Wschebor (2002)

ESAIM: Probability and Statistics

Similarity:

We study the tails of the distribution of the maximum of a stationary gaussian process on a bounded interval of the real line. Under regularity conditions including the existence of the spectral moment of order 8, we give an additional term for this asymptotics. This widens the application of an expansion given originally by Piterbarg [11] for a sufficiently small interval.

Explicit Karhunen-Loève expansions related to the Green function of the Laplacian

J.-R. Pycke (2006)

Banach Center Publications

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Karhunen-Loève expansions of Gaussian processes have numerous applications in Probability and Statistics. Unfortunately the set of Gaussian processes with explicitly known spectrum and eigenfunctions is narrow. An interpretation of three historical examples enables us to understand the key role of the Laplacian. This allows us to extend the set of Gaussian processes for which a very explicit Karhunen-Loève expansion can be derived.