Asymptotic behaviour for a time-inhomogeneous Kolmogorov type diffusion

Mihai Gradinaru; Emeline Luirard

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arXiv · 2004.11576

Asymptotic behaviour for a time-inhomogeneous Kolmogorov type diffusion

Mihai Gradinaru·Emeline Luirard

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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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BibTeX RIS

Mihai Gradinaru, Emeline Luirard. 2020-04-24. Asymptotic behaviour for a time-inhomogeneous Kolmogorov type diffusion. https://arxiv.org/abs/2004.11576

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