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