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Anomalous diffusion behaviour for a time-inhomogeneous Kolmogorov type diffusion

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02552764
Contributor : Emeline Luirard Connect in order to contact the contributor
Submitted on : Thursday, June 4, 2020 - 9:59:40 AM
Last modification on : Friday, May 20, 2022 - 9:04:51 AM

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  • HAL Id : hal-02552764, version 2
  • ARXIV : 2004.11576

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Mihai Gradinaru, Emeline Luirard. Anomalous diffusion behaviour for a time-inhomogeneous Kolmogorov type diffusion. 2020. ⟨hal-02552764v2⟩

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