On the spectrum of Markov semigroups via sample path large deviations

Details On the spectrum of Markov semigroups via sample path large deviations On the spectrum of Markov semigroups via sample path large deviations

2004-11-10

arxiv.org/abs/math/0411221v1

Probability Theory and Related Fields, 2006, V 134, n 11, pp 44-80

Mathematics

Probability

32 pages, 1 figure, to be published in "Probability Theory and Related Fields"

Scientific paper

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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