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On the spectrum of Markov semigroups via sample path large deviations
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  • Published: 10 February 2005

On the spectrum of Markov semigroups via sample path large deviations

  • Irina Ignatiouk-Robert1 

Probability Theory and Related Fields volume 134, pages 44–80 (2006)Cite this article

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  • 2 Citations

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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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Authors and Affiliations

  1. Université de Cergy-Pontoise, Département de Mathématiques, 2, Avenue Adolphe Chauvin, 95302, Cergy-Pontoise Cedex, France

    Irina Ignatiouk-Robert

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  1. Irina Ignatiouk-Robert
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Correspondence to Irina Ignatiouk-Robert.

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Cite this article

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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  • Received: 15 June 2004

  • Revised: 11 November 2004

  • Published: 10 February 2005

  • Issue Date: January 2006

  • DOI: https://doi.org/10.1007/s00440-004-0410-7

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Key words or phrases

  • Spectral radius
  • Sample path large deviations
  • Convergence parameter
  • Cluster expansions

Mathematics Subject Classification (1991)

  • Primary 60F10
  • Secondary 60J15
  • 60K35
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