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Pré-Publication, Document De Travail Année : 2021

Anomalous diffusion behaviour for a time-inhomogeneous Kolmogorov type diffusion

Résumé

We study a kinetic stochastic model with a non-linear time-inhomogeneous drag force and a Brownian-type random force. More precisely, the Kolmogorov type diffusion $(V,X)$ is considered. Here $X$ is the position of the particle and $V$ is its velocity and is solution of a stochastic differential equation driven by a one-dimensional Brownian motion, with the drift of the form $t^{-\beta}F(v)$. The function $F$ satisfies some homogeneity condition and $\beta$ is positive. The behaviour of the process $(V,X)$ in large time is proved 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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Mihai Gradinaru, Emeline Luirard. Anomalous diffusion behaviour for a time-inhomogeneous Kolmogorov type diffusion. 2021. ⟨hal-02552764v3⟩
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