Diffusive behaviour for some time-inhomogeneous stochastic kinetic models
Résumé
In this paper, we consider a kinetic stochastic model with a non-linear time-inhomogeneous drag force and a Brownian random force. More precisely, we study the position $X_t$ of a particle having the velocity as 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 diffusive behaviour of the position in large time is proven and the precise rate of convergence is pointed out by using stochastic analysis tools.
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