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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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Dates and 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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Cite

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