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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 82, 2010 - Issue 1: Special issue on Filtering and Stochastic Control
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Original Articles

On discrete time ergodic filters with wrong initial data, 2

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Pages 25-40 | Received 03 Dec 2007, Accepted 14 Oct 2008, Published online: 16 Feb 2010
 

Abstract

For a class of non-uniformly ergodic Markov chains satisfying exponential or polynomial beta-mixing, under observations subject to an IID noise, it is shown that wrong initial data is forgotten in the mean total variation topology, with a certain exponential or polynomial rate. It is allowed that the density of the noise in the signal may vanish.

AMS Subject Classification::

Acknowledgements

The authors are grateful to the anonymous referee for useful remarks. The second author thanks the grant RFBR 08-01-00105a for support.

Notes

Additional information

Notes on contributors

M.L. Kleptsyna

1. 1. [email protected]

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