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Asymptotic 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 by using stochastic analysis tools.
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Contributor : Emeline Luirard Connect in order to contact the contributor
Submitted on : Monday, March 14, 2022 - 11:57:05 AM
Last modification on : Friday, May 20, 2022 - 9:04:52 AM


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  • HAL Id : hal-02552764, version 5
  • ARXIV : 2004.11576


Mihai Gradinaru, Emeline Luirard. Asymptotic behaviour for a time-inhomogeneous Kolmogorov type diffusion. 2022. ⟨hal-02552764v5⟩



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