Uniform time average consistency of Monte Carlo particle filters

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Abstract

We prove that bootstrap-type Monte Carlo particle filters approximate the optimal nonlinear filter in a time average sense uniformly with respect to the time horizon when the signal is ergodic and the particle system satisfies a tightness property. The latter is satisfied without further assumptions when the signal state space is compact, as well as in the noncompact setting when the signal is geometrically ergodic and the observations satisfy additional regularity assumptions.

Original languageEnglish (US)
Pages (from-to)3835-3861
Number of pages27
JournalStochastic Processes and their Applications
Volume119
Issue number11
DOIs
StatePublished - Nov 1 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Bootstrap Monte Carlo filter
  • Interacting particles
  • Nonlinear filter
  • Uniform convergence

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