Spectral gaps and exponential integrability of hitting times for linear diffusions
type: Item
instance of: scholarly article
title: Spectral gaps and exponential integrability of hitting times for linear diffusions
zbMATH Open document ID: 1233.60044
DOI: 10.1214/10-AIHP380
author: Oleg Loukianov
author: Dasha Loukianova
author: Shiqi Song
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2011-10-11T00:00:00Z
full work available at URL: https://eudml.org/doc/243348
review text: Let \((X_t) _ {t \geq 0}\) be a regular, positively recurrent and conservative Markov process with state space \(\mathbb{R}\). Using the quantities \[ B_ {a}^ {+} : = \sup _ {x \geq a} m ( (x, +\infty ))(S(x) - S(a)) ;\;B_ {a}^ {-} : = \sup _ {x \leq a} m ( (-\infty , x))(S(a) - S(x)), \] where \(S\) is a scale function of \(X\) and \(m\) is the speed measure associated with \(S\), the authors are able to provide a two-sided estimate for the exponential moments of hitting times. Then, they establish a direct relation between exponential moments and spectral gaps of generators associated with \(X\), improving the classical bounds. The final part of the paper illustrates the authors' results for some particular processes, such as drifted Brownian motions and Ornstein-Uhlenbeck processes.
reviewed by: Liliana Popa
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 5956523
zbMATH Keywords: recurrence
zbMATH Keywords: linear Markov process
zbMATH Keywords: exponential moments
zbMATH Keywords: hitting times
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: spectral gap
zbMATH Keywords: Dirichlet form
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5956523