On discrete time ergodic filters with wrong initial data, 2

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.

Keywords:

• non-linear filtering
• wrong initial data
• stability of filters

AMS Subject Classification::

• Primary 60G35; 62M20
• Secondary 93E11; 93E15

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

^1. [email protected]

Additional information

Notes on contributors

M.L. Kleptsyna

1. 1. [email protected]