Displaying similar documents to “Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix”

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.

The renormalization transformation for two-type branching models

D. A. Dawson, A. Greven, F. den Hollander, Rongfeng Sun, J. M. Swart (2008)

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

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This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting within colonies. Their large-scale space–time behavior can be studied by means of a renormalization program. This program, which has been carried out successfully in a number of other cases (mostly one-dimensional), is based on the construction and the...

Variance decay for functionals of the environment viewed by the particle

Jean-Christophe Mourrat (2011)

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

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For the random walk among random conductances, we prove that the environment viewed by the particle converges to equilibrium polynomially fast in the variance sense, our main hypothesis being that the conductances are bounded away from zero. The basis of our method is the establishment of a Nash inequality, followed either by a comparison with the simple random walk or by a more direct analysis based on a martingale decomposition. As an example of application, we show that under certain...

A stochastic approach to relativistic diffusions

Ismaël Bailleul (2010)

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

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A new class of relativistic diffusions encompassing all the previously studied examples has recently been introduced in the article of C. Chevalier and F. Debbasch (J. Math. Phys. (2008) 043303), both in a heuristic and analytic way. A stochastic approach of these processes is proposed here, in the general framework of lorentzian geometry. In considering the dynamics of the random motion in strongly causal spacetimes, we are able to give a simple definition of the one-particle distribution...