Exponential stability in discrete-time filtering for non-ergodic signals

A. Budhiraja, D. Ocone

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

In this paper we prove exponential asymptotic stability for discrete-time filters for signals arising as solutions of d-dimensional stochastic difference equations. The observation process is the signal corrupted by an additive white noise of sufficiently small variance. The model for the signal admits non-ergodic processes. We show that almost surely, the total variation distance between the optimal filter and an incorrectly initialized filter converges to 0 exponentially fast as time approaches ∞.

Original languageEnglish (US)
Pages (from-to)245-257
Number of pages13
JournalStochastic Processes and their Applications
Volume82
Issue number2
DOIs
StatePublished - Aug 1 1999

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Asymptotic stability
  • Measure valued processes
  • Nonlinear filtering

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