منابع مشابه
Poincaré inequalities and hitting times
Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions are well known. We give here the correspondance (with quantitative results) for reversible diffusion processes. As a consequence, we generalize results of Bobkov in the one dimensional case on the value of the Poincaré constant for logconcave measures to superlinear potentials. Finally, we study ...
متن کاملHitting Times, Functional Inequalities, Lyapunov Conditions and Uniform Ergodicity
The use of Lyapunov conditions for proving functional inequalities was initiated in [5]. It was shown in [4, 30] that there is an equivalence between a Poincaré inequality, the existence of some Lyapunov function and the exponential integrability of hitting times. In the present paper, we close the scheme of the interplay between Lyapunov conditions and functional inequalities by • showing that...
متن کاملTight Inequalities among Set Hitting times in Markov Chains
Given an irreducible discrete-time Markov chain on a finite state space, we consider the largest expected hitting time T (α) of a set of stationary measure at least α for α ∈ (0, 1). We obtain tight inequalities among the values of T (α) for different choices of α. One consequence is that T (α) ≤ T (1/2)/α for all α < 1/2. As a corollary we have that, if the chain is lazy in a certain sense as ...
متن کاملAsymptotics for Hitting Times
In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class (A) F = F is continuous and concave; F (t) ≤ t for t ≥ 0.. Note that all possible asymptotics are absolutely continuous.
متن کاملOn Friedrichs – Poincaré - type inequalities ✩
Friedrichsand Poincaré-type inequalities are important and widely used in the area of partial differential equations and numerical analysis. Most of their proofs appearing in references are the argument of reduction to absurdity. In this paper, we give direct proofs of Friedrichs-type inequalities in H 1(Ω) and Poincaré-type inequalities in some subspaces of W1,p(Ω). The dependencies of the ine...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
سال: 2013
ISSN: 0246-0203
DOI: 10.1214/11-aihp447