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Anomalous diffusion behaviour for a time-inhomogeneous Kolmogorov type diffusion

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02552764
Contributor : Emeline Luirard Connect in order to contact the contributor
Submitted on : Monday, July 5, 2021 - 9:51:53 PM
Last modification on : Friday, May 20, 2022 - 9:04:51 AM

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  • HAL Id : hal-02552764, version 4
  • ARXIV : 2004.11576

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Mihai Gradinaru, Emeline Luirard. Anomalous diffusion behaviour for a time-inhomogeneous Kolmogorov type diffusion. 2021. ⟨hal-02552764v4⟩

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