Open Access
Translator Disclaimer
2020 Homogenisation for anisotropic kinetic random motions
Pierre Perruchaud
Electron. J. Probab. 25: 1-26 (2020). DOI: 10.1214/20-EJP439


We introduce a class of kinetic and anisotropic random motions $(x_{t}^{\sigma },v_{t}^{\sigma })_{t \geq 0}$ on the unit tangent bundle $T^{1} \mathcal{M} $ of a general Riemannian manifold $(\mathcal{M} ,g)$, where $\sigma $ is a positive parameter quantifying the amount of noise affecting the dynamics. As the latter goes to infinity, we then show that the time rescaled process $(x_{\sigma ^{2} t}^{\sigma })_{t \geq 0}$ converges in law to an explicit anisotropic Brownian motion on $\mathcal{M} $. Our approach is essentially based on the strong mixing properties of the underlying velocity process and on rough paths techniques, allowing us to reduce the general case to its Euclidean analogue. Using these methods, we are able to recover a range of classical results.


Download Citation

Pierre Perruchaud. "Homogenisation for anisotropic kinetic random motions." Electron. J. Probab. 25 1 - 26, 2020.


Received: 21 November 2018; Accepted: 2 March 2020; Published: 2020
First available in Project Euclid: 31 March 2020

zbMATH: 07206376
MathSciNet: MR4089789
Digital Object Identifier: 10.1214/20-EJP439

Primary: 58J65 , 60G51 , 60H10

Keywords: Diffusion processes , Homogenization‎ , Mixing , Riemannian manifolds , Rough paths theory


Vol.25 • 2020
Back to Top