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Journal Articles Discrete and Continuous Dynamical Systems - Series A Year : 2023

Scaling limit of a kinetic inhomogeneous stochastic system in the quadratic potential

Abstract

We consider a particle evolving in the quadratic potential and subject to a time-inhomogeneous frictional force and to a random force. The couple of its velocity and position is solution to a stochastic differential equation driven by an $\alpha$-stable Lévy process with $\alpha \in (1,2]$ and the frictional force is of the form $t^{-\beta}\text{sgn}(v)|v|^\gamma$. We identify three regimes for the behavior in long-time of the couple velocity-position with a suitable rescaling, depending on the balance between the frictional force and the index of stability $\alpha$ of the noise.
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Dates and versions

hal-03703246 , version 1 (23-06-2022)
hal-03703246 , version 2 (04-03-2023)

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Thomas Cavallazzi, Emeline Luirard. Scaling limit of a kinetic inhomogeneous stochastic system in the quadratic potential. Discrete and Continuous Dynamical Systems - Series A, 2023, ⟨10.3934/dcds.2023042⟩. ⟨hal-03703246v2⟩
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