arXiv subjects

Emeline Luirard

Publications and source records attributed to Emeline Luirard.

3 recordsLinked to original sources

arXiv2022

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

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 L{\'e}vy 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.

math.PR↗

arXiv2021

Kinetic time-inhomogeneous L{\'e}vy-driven model

We study a one-dimensional kinetic stochastic model driven by a L{\'e}vy 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 L{\'e}vy process of index $\alpha$ or a general L{\'e}vy 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.

math.PR↗

arXiv2020

Asymptotic behaviour for a time-inhomogeneous Kolmogorov type diffusion

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.

math.PR↗