Anomalous diffusion behaviour for a time-inhomogeneous Kolmogorov type diffusion
Résumé
We consider a kinetic stochastic model with a non-linear time-inhomogeneous drag force and a Brownian random force. More precisely, we study the couple position $X_t$ of a particle and its velocity which is a solution of a stochastic differential equation driven by a one-dimensional Brownian motion, with the drift of the form $t^{-\beta}F(v)$, $F$ satisfying some homogeneity condition and $\beta>0$. The behaviour of $(V,X)$ in large time is proven and the precise rate of convergence is pointed out by using stochastic analysis tools.
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