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Quasi-compactness and absolutely continuous kernels
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  • Published: 22 December 2006

Quasi-compactness and absolutely continuous kernels

  • Hubert Hennion1 

Probability Theory and Related Fields volume 139, pages 451–471 (2007)Cite this article

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  • 6 Citations

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Abstract

We show how the essential spectral radius r e (Q) of a bounded positive kernel Q, acting on bounded functions, is linked to the lower approximation of Q by certain absolutely continuous kernels. The standart Doeblin’s condition can be interpreted in this context, and, when suitably reformulated, it leads to a formula for r e (Q). This results may be used to characterize the Markov kernels having a quasi-compact action on a space of measurable functions bounded with respect to some test function, when no irreducibilty and aperiodicity are assumed.

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Authors and Affiliations

  1. IRMAR, Université de Rennes I, Campus de Beaulieu, 35042, Rennes-Cedex, France

    Hubert Hennion

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  1. Hubert Hennion
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Correspondence to Hubert Hennion.

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Hennion, H. Quasi-compactness and absolutely continuous kernels. Probab. Theory Relat. Fields 139, 451–471 (2007). https://doi.org/10.1007/s00440-006-0048-8

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  • Received: 19 September 2004

  • Revised: 09 November 2006

  • Published: 22 December 2006

  • Issue Date: November 2007

  • DOI: https://doi.org/10.1007/s00440-006-0048-8

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Keywords

  • Markov chain
  • Quasi-compactness
  • Positive operator

Mathematics Subject Classification (2000)

  • 60J05
  • 47B07
  • 47B65
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