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# Kinetic time-inhomogeneous Lévy-driven model

Abstract : We study a one-dimensional kinetic stochastic model driven by a Lévy process with a non-linear time-inhomogeneous drift. More precisely, the process $(V,X)$ is considered, where $X$ is the position of the particle and its velocity $V$ is the solution of a stochastic differential equation with a drift of the form $t^{-\beta}F(v)$. The driving process can be a stable Lévy process of index $\alpha$ or a general Lévy process under appropriate assumptions. The function $F$ satisfies a homogeneity condition and $\beta$ is non-negative. The behavior in large time of the process $(V,X)$ is proved and the precise rate of convergence is pointed out by using stochastic analysis tools. To this end, we compute the moment estimates of the velocity process.
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https://hal.archives-ouvertes.fr/hal-03478268
Contributor : Emeline Luirard Connect in order to contact the contributor
Submitted on : Thursday, April 21, 2022 - 4:52:31 PM
Last modification on : Friday, May 20, 2022 - 9:04:52 AM

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### Identifiers

• HAL Id : hal-03478268, version 3
• ARXIV : 2112.07287

### Citation

Mihai Gradinaru, Emeline Luirard. Kinetic time-inhomogeneous Lévy-driven model. 2022. ⟨hal-03478268v3⟩

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