| Issue |
ESAIM: PS
Volume 27, 2023
|
|
|---|---|---|
| Page(s) | 1 - 18 | |
| DOI | https://doi.org/10.1051/ps/2022014 | |
| Published online | 06 January 2023 | |
Asymptotic behavior for a time-inhomogeneous Kolmogorov type diffusion
Univ Rennes, CNRS, IRMAR - UMR 6625,
35000
Rennes, France
* Corresponding author: emeline.luirard@orange.fr
Received:
25
March
2021
Accepted:
27
October
2022
We study a kinetic stochastic model with a non-linear time-inhomogeneous friction force and a Brownian-type random force. More precisely, a Kolmogorov type diffusion (V, X) is considered: here, X is the position of the particle, and V is its velocity. The process V is solution to a stochastic differential equation driven by a one-dimensional Brownian motion, with a drift of the form t−βF(v). The function F satisfies some homogeneity condition, and β is a real number. The behavior in large time of the process (V, X) is proved by using stochastic analysis tools.
Mathematics Subject Classification: 60J60 / 60H10 / 60J65 / 60F17
Key words: Kinetic stochastic equation / time-inhomogeneous diffusion / explosion time / scaling transformation / asymptotic distribution / ergodicity
© The authors. Published by EDP Sciences, SMAI 2023
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