Article contents
Stability with respect to initial conditions in V-norm for nonlinear filters with ergodic observations
Published online by Cambridge University Press: 04 April 2017
Abstract
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.
MSC classification
- Type
- Research Papers
- Information
- Copyright
- Copyright © Applied Probability Trust 2017
References
- 3
- Cited by