Displaying similar documents to “Properties of local-nondeterminism of Gaussian and stable random fields and their applications”

Invariance principle, multifractional gaussian processes and long-range dependence

Serge Cohen, Renaud Marty (2008)

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

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This paper is devoted to establish an invariance principle where the limit process is a multifractional gaussian process with a multifractional function which takes its values in (1/2, 1). Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional brownian motion.

Random fractals generated by a local gaussian process indexed by a class of functions

Claire Coiffard (2011)

ESAIM: Probability and Statistics

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In this paper, we extend the results of Orey and Taylor [S. Orey and S.J. Taylor, How often on a Brownian path does the law of the iterated logarithm fail? 28 (1974) 174–192] relative to random fractals generated by oscillations of Wiener processes to a multivariate framework. We consider a setup where Gaussian processes are indexed by classes of functions.

Long memory and self-similar processes

Gennady Samorodnitsky (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.

Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations

Renaud Marty (2010)

ESAIM: Probability and Statistics

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We consider a differential equation with a random rapidly varying coefficient. The random coefficient is a Gaussian process with slowly decaying correlations and compete with a periodic component. In the asymptotic framework corresponding to the separation of scales present in the problem, we prove that the solution of the differential equation converges in distribution to the solution of a stochastic differential equation driven by a classical Brownian motion in some cases, by a fractional...