Ornstein-uhlenbeck Pinball: I. Poincaré Inequalities in a Punctured Domain
نویسندگان
چکیده
In this paper we study the Poincaré constant for the Gaussian measure restricted to D = R − B(y, r) where B(y, r) denotes the Euclidean ball with center y and radius r, and d ≥ 2. We also study the case of the l 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.
منابع مشابه
On the Ornstein-Uhlenbeck operator in convex sets of Banach spaces
We study the Ornstein-Uhlenbeck operator and the Ornstein-Uhlenbeck semigroup in an open convex subset of an infinite dimensional separable Banach space X. This is done by finite dimensional approximation. In particular we prove Logarithmic-Sobolev and Poincaré inequalities, and thanks to these inequalities we deduce spectral properties of the OrnsteinUhlenbeck operator. 2010 Mathematics Subjec...
متن کاملDeviation Inequalities and Moderate Deviations for Estimators of Parameters in an Ornstein-uhlenbeck Process with Linear Drift
DEVIATION INEQUALITIES AND MODERATE DEVIATIONS FOR ESTIMATORS OF PARAMETERS IN AN ORNSTEIN-UHLENBECK PROCESS WITH LINEAR DRIFT FUQING GAO School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P.R.China email: [email protected] HUI JIANG School of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China email: [email protected] Submitted December 2...
متن کاملBinomial-Poisson entropic inequalities and the M/M/∞ queue
This article provides entropic inequalities for binomial-Poisson distributions, derived from the two point space. They appear as local inequalities of the M/M/∞ queue. They describe in particular the exponential dissipation of Φ-entropies along this process. This simple queueing process appears as a model of “constant curvature”, and plays for the simple Poisson process the role played by the O...
متن کاملFractional Poincaré Inequalities for General Measures
We prove a fractional version of Poincaré inequalities in the context of R endowed with a fairly general measure. Namely we prove a control of an L norm by a non local quantity, which plays the role of the gradient in the standard Poincaré inequality. The assumption on the measure is the fact that it satisfies the classical Poincaré inequality, so that our result is an improvement of the latter...
متن کاملLogarithmic Sobolev inequality for diffusion semigroups
Through the main example of the Ornstein-Uhlenbeck semigroup, the Bakry-Emery criterion is presented as a main tool to get functional inequalities as Poincaré or logarithmic Sobolev inequalities. Moreover an alternative method using the optimal mass transportation, is also given to obtain the logarithmic Sobolev inequality. Mathematics Subject Classification (2000) : Primary 35B40, 35K10, 60J60.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013