Kinetic timeinhomogeneous L{é}vydriven model
Abstract
We study a onedimensional kinetic stochastic model driven by a L{é}vy process with a nonlinear timeinhomogeneous 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{é}vy process of index $\alpha$ or a general L{é}vy process under appropriate assumptions. The function $F$ satisfies a homogeneity condition and $\beta$ is nonnegative. 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 DOI:
 10.48550/arXiv.2112.07287
 arXiv:
 arXiv:2112.07287
 Bibcode:
 2021arXiv211207287G
 Keywords:

 Mathematics  Probability