Displaying similar documents to “Diffusion in long-range correlated Ornstein-Uhlenbeck flows.”

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

Renaud Marty (2005)

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...

On homogenization of space-time dependent and degenerate random flows II

Rémi Rhodes (2008)

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

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We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In (2007) (to appear), an invariance principle is proved for the critical rescaling of the diffusion. Here, we generalize this approach to diffusions whose space-time scaling differs from the critical one.

Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix

Rémi Rhodes (2009)

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

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This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [ (2009)] and improves this latter work by considering possibly...