Ornstein-Uhlenbeck pinball: I. Poincaré inequalities in a punctured domain

Emmanuel Boissard; Patrick Cattiaux; Arnaud Guillin; Laurent Miclo

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arXiv · 1309.0986

Ornstein-Uhlenbeck pinball: I. Poincaré inequalities in a punctured domain

Emmanuel Boissard·Patrick Cattiaux·Arnaud Guillin·Laurent Miclo

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Abstract

In this paper we study the Poincaré constant for the Gaussian measure restricted to $D=\R^d - B(y,r)$ where $B(y,r)$ denotes the Euclidean ball with center $y$ and radius $r$, and $d\geq 2$. We also study the case of the $l^\infty$ ball (the hypercube). This is the first step in the study of the asymptotic behavior of a $d$-dimensional Ornstein-Uhlenbeck process in the presence of obstacles with elastic normal reflections (the Ornstein-Uhlenbeck pinball) we shall study in a companion paper.

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BibTeX RIS

Emmanuel Boissard, Patrick Cattiaux, Arnaud Guillin, Laurent Miclo. 2013-09-04. Ornstein-Uhlenbeck pinball: I. Poincaré inequalities in a punctured domain. https://arxiv.org/abs/1309.0986

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