Stability of Optimal Filter Higher-Order Derivatives

Vladislav Z. B. Tadić, Arnaud Doucet

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

2 Citations (Scopus)
8 Downloads (Pure)


In many scenarios, a state-space model depends on a parameter which needs to be inferred from data. Using stochastic gradient search and the optimal filter (first-order) derivative, the parameter can be estimated online. To analyze the asymptotic behavior of online methods for parameter estimation in non-linear state-space models, it is necessary to establish results on the existence and stability of the optimal filter higher-order derivatives. The existence and stability properties of these derivatives are studied here. We show that the optimal filter higher-order derivatives exist and forget initial conditions exponentially fast. We also show that the optimal filter higher-order derivatives are geometrically ergodic. The obtained results hold under (relatively) mild conditions and apply to state-space models met in practice.
Original languageEnglish
JournalStochastic Processes and their Applications
Early online date7 Feb 2020
Publication statusE-pub ahead of print - 7 Feb 2020


  • state-space models
  • optimal filter
  • optimal filter higher-order derivatives
  • forgetting of initial conditions
  • geometric ergodicity
  • log-likelihood


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