On the spectrum of Markov semigroups via sample path large deviations |
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Authors: | Irina Ignatiouk-Robert |
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Institution: | (1) Université de Cergy-Pontoise, Département de Mathématiques, 2, Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France |
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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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Keywords: | Spectral radius Sample path large deviations Convergence parameter Cluster expansions |
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