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Stability of optimal filter higher-order derivatives

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  • Tadić, Vladislav Z.B.
  • Doucet, Arnaud

Abstract

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 derivatives, the parameter can be estimated online. To analyze the asymptotic behavior of such methods, it is necessary to establish results on the existence and stability of the optimal filter higher-order derivatives. These properties are studied here. Under regularity conditions, we show that the optimal filter higher-order derivatives exist and forget initial conditions exponentially fast. We also show that the same derivatives are geometrically ergodic.

Suggested Citation

  • Tadić, Vladislav Z.B. & Doucet, Arnaud, 2020. "Stability of optimal filter higher-order derivatives," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4808-4858.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:8:p:4808-4858
    DOI: 10.1016/j.spa.2020.02.001
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    References listed on IDEAS

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    1. Tadic, Vladislav B. & Doucet, Arnaud, 2005. "Exponential forgetting and geometric ergodicity for optimal filtering in general state-space models," Stochastic Processes and their Applications, Elsevier, vol. 115(8), pages 1408-1436, August.
    2. Rydén, Tobias, 1997. "On recursive estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 79-96, February.
    3. George Poyiadjis & Arnaud Doucet & Sumeetpal S. Singh, 2011. "Particle approximations of the score and observed information matrix in state space models with application to parameter estimation," Biometrika, Biometrika Trust, vol. 98(1), pages 65-80.
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