Hypocoercive estimates on foliations and velocity spherical Brownian\n motion

2016/04/22 by Fabrice Baudoin, Baudoin, Fabrice, Camille Tardif +1
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1604.06813

openalex publication_date 2016/04/22 · openalex created_date 2019/07/30 · openalex updated_date 2026/08/01

Abstract

By further developing the generalized \Γ-calculus for hypoelliptic\noperators, we prove hypocoercive estimates for a large class of Kolmogorov type\noperators which are defined on non necessarily totally geodesic Riemannian\nfoliations. We study then in detail the example of the velocity spherical\nBrownian motion, whose generator is a step-3 generating hypoelliptic\nH "ormander's type operator. To prove hypocoercivity in that case, the key\npoint is to show the existence of a convenient Riemannian foliation associated\nto the diffusion. We will then deduce, under suitable geometric conditions, the\nconvergence to equilibrium of the diffusion in H¹ and in L².\n

Citations

• Isotropic Hypoellipticity and Trend to Equilibrium for the Fokker-Planck Equation with a High-Degree Potential

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