We establish conditions for an exponential rate of forgetting of the initial distribution of nonlinear filters in V-norm, allowing for unbounded test functions. The analysis is conducted in an general setup involving nonnegative kernels in a random environment which allows treatment of filters and prediction filters in a single framework. The main result is illustrated on two examples, the first showing that a total variation norm stability result obtained by Douc et al. (2009) can be extended to V-norm without any additional assumptions, the second concerning a situation in which forgetting of the initial condition holds in V-norm for the filters, but the V-norm of each prediction filter is infinite.
|Number of pages||16|
|Journal||Journal of Applied Probability|
|Publication status||Published - 4 Apr 2017|
- hidden Markov model
- Nonlinear filtering
- random environment
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Professor Nick Whiteley
- School of Mathematics - Heilbronn Chair in Data Science
- Statistical Science
- Probability, Analysis and Dynamics
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