Abstract
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.
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Ignatiouk-Robert, I. On the spectrum of Markov semigroups via sample path large deviations. Probab. Theory Relat. Fields 134, 44–80 (2006). https://doi.org/10.1007/s00440-004-0410-7
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DOI: https://doi.org/10.1007/s00440-004-0410-7
Key words or phrases
- Spectral radius
- Sample path large deviations
- Convergence parameter
- Cluster expansions
Mathematics Subject Classification (1991)
- Primary 60F10
- Secondary 60J15
- 60K35