Accelerating planar Ornstein-Uhlenbeck diffusion with suitable drift

Mondher Damak; Brice Franke; Nejib Yaakoubi

doi:10.3934/dcds.2020173

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2020, Volume 40, Issue 7: 4093-4112. Doi: 10.3934/dcds.2020173

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Accelerating planar Ornstein-Uhlenbeck diffusion with suitable drift

1.
Laboratoire d'Algèbre, Géométrie, Théorie Spectrale LR 11 ES 53, Faculté des Sciences de Sfax, Univerité de Sfax, 3.5 km, Route de la Soukra, B.P. 1171, Sfax 3000, Tunisia
2.
Laboratoire de Mathématiques de Bretagne Atlantique, UMR CNRS 6205, Université de Brest, UFR Sciences et Techniques, 6 Avenue Le Gorgeu, 29200 Brest, France
3.
ESPRIT - Ecole Supérieure Privée d'Ingénierie et de Technologies, Pôle Technologique El Ghazela, Ariana 2083, Tunisia

^* Corresponding author: Brice Franke
^* Corresponding author: Brice Franke

Received: June 2018

Revised: February 2019

Published online: July 2020

This research was supported by the french tunisian research grant PHC Utique CMCU16G1505.

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Abstract

The principal aim of this paper is to construct an explicit sequence of weighted divergence free vector fields which accelerates the rate of convergence of planar Ornstein-Uhlenbeck diffusion to its equilibrium state. The rate of convergence is expressed in terms of the spectral gap of the diffusion generator. We construct an explicit sequence of vector fields which pushes the spectral gap to infinity. The acceleration of the diffusion results from the strong oscillation of the flow lines generated by the vector field.

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Mathematics Subject Classification: Primary: 62M15; Secondary: 58J65, 47D03.

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