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 brownian...

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 Brownian
motion...

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.

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