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Article Dans Une Revue ESAIM: Probability and Statistics Année : 2023

Asymptotic behavior for a time-inhomogeneous Kolmogorov type diffusion

Résumé

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.
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Dates et versions

hal-03928217 , version 1 (06-01-2023)

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Citer

Mihai Gradinaru, Emeline Luirard. Asymptotic behavior for a time-inhomogeneous Kolmogorov type diffusion. ESAIM: Probability and Statistics, 2023, 27, pp.1-18. ⟨10.1051/ps/2022014⟩. ⟨hal-03928217⟩
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