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Pré-Publication, Document De Travail Année : 2020

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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Dates et versions

hal-02552764 , version 1 (23-04-2020)
hal-02552764 , version 2 (04-06-2020)
hal-02552764 , version 3 (26-03-2021)
hal-02552764 , version 4 (05-07-2021)
hal-02552764 , version 5 (14-03-2022)

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Citer

Mihai Gradinaru, Emeline Luirard. Diffusive behaviour for some time-inhomogeneous stochastic kinetic models. 2020. ⟨hal-02552764v1⟩
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