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Identification of Continuous-Discrete Hidden Markov Models with Multiplicative Observation Noise

Author

Listed:
  • Andrey Borisov

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilova str. 44/2, 119333 Moscow, Russia)

  • Andrey Gorshenin

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vavilova str. 44/2, 119333 Moscow, Russia)

Abstract

The paper aims to identify hidden Markov model parameters. The unobservable state represents a finite-state Markov jump process. The observations contain Wiener noise with state-dependent intensity. The identified parameters include the transition intensity matrix of the system state, conditional drift and diffusion coefficients in the observations. We propose an iterative identification algorithm based on the fixed-interval smoothing of the Markov state. Using the calculated state estimates, we restore all required system parameters. The paper contains a detailed description of the numerical schemes of state estimation and parameter identification. The comprehensive numerical study confirms the high precision of the proposed identification estimates.

Suggested Citation

  • Andrey Borisov & Andrey Gorshenin, 2022. "Identification of Continuous-Discrete Hidden Markov Models with Multiplicative Observation Noise," Mathematics, MDPI, vol. 10(17), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3062-:d:897263
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    References listed on IDEAS

    as
    1. Ishikawa, Yasushi & Kunita, Hiroshi, 2006. "Malliavin calculus on the Wiener-Poisson space and its application to canonical SDE with jumps," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1743-1769, December.
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    Cited by:

    1. Andrey Borisov & Alexey Ivanov, 2023. "Stochastic Time Complexity Surfaces of Computing Node," Mathematics, MDPI, vol. 11(20), pages 1-26, October.

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