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On discrete time ergodic filters with wrong initial data
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  • Published: 24 August 2007

On discrete time ergodic filters with wrong initial data

  • M. L. Kleptsyna1 &
  • A. Yu. Veretennikov2,3 

Probability Theory and Related Fields volume 141, pages 411–444 (2008)Cite this article

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  • 23 Citations

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Abstract

For a class of non-uniformly ergodic Markov chains (X n ) satisfying exponential or polynomial beta-mixing, under observations (Y n ) subject to an IID noise with a positive density, it is shown that wrong initial data is forgotten in the mean total variation topology, with a certain exponential or polynomial rate.

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Authors and Affiliations

  1. Université du Maine, Le Mans, France

    M. L. Kleptsyna

  2. School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK

    A. Yu. Veretennikov

  3. Institute of Information Transmission Problems, Moscow, Russia

    A. Yu. Veretennikov

Authors
  1. M. L. Kleptsyna
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  2. A. Yu. Veretennikov
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Corresponding author

Correspondence to A. Yu. Veretennikov.

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Cite this article

Kleptsyna, M.L., Veretennikov, A.Y. On discrete time ergodic filters with wrong initial data. Probab. Theory Relat. Fields 141, 411–444 (2008). https://doi.org/10.1007/s00440-007-0089-7

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  • Received: 13 October 2005

  • Revised: 05 June 2007

  • Published: 24 August 2007

  • Issue Date: July 2008

  • DOI: https://doi.org/10.1007/s00440-007-0089-7

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Mathematics Subject Classification (2000)

  • 60G35
  • 62M20
  • 93E11
  • 93E15
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