Stability with respect to initial conditions in V-norm for nonlinear filters with ergodic observations

Mathieu Gerber, Nick Whiteley*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)
304 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)118-133
Number of pages16
JournalJournal of Applied Probability
Volume54
Issue number1
DOIs
Publication statusPublished - 4 Apr 2017

Keywords

  • hidden Markov model
  • Nonlinear filtering
  • random environment
  • V-norm

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