On the spectrum of Markov semigroups via sample path large deviations

• 成果类型: Article
• 署名作者: Ignatiouk-Robert, I
• 署名单位: CY Cergy Paris Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0410-7
• 发表日期: 2006
• 页码: 44-80
• 关键词: ergodic properties

摘要

The essential spectral radius of a sub-Markovian process is defined as the infimum of the spectral radiuses of all local perturbations of the process. When the family of rescaled processes satisfies sample path large deviation principle, the spectral radius and the essential spectral radius are expressed in terms of the rate function. The paper is motivated by applications to reflected diffusions and jump Markov processes describing stochastic networks for which the sample path large deviation principle has been established and the rate function has been identified while essential spectral radius has not been calculated.