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Quasi-exact Approximation of Hidden Markov Chain Filters



This paper studies the application of exact simulation methods for multi-dimensional multiplicative noise stochastic differential equations to filtering. Stochastic differential equations with multiplicative noise naturally occur as Zakai equation in hidden Markov chain filtering. The paper proposes a quasi-exact approximation method for hidden Markov chain filters, which can be applied when discrete time approximations, such as the Euler scheme, may fail in practice.

Suggested Citation

  • Eckhard Platen & Renata Rendek, 2009. "Quasi-exact Approximation of Hidden Markov Chain Filters," Research Paper Series 258, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:258

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    References listed on IDEAS

    1. Fischer Paul & Platen Eckhard, 1999. "Applications of the balanced method to stochastic differential equations in filtering," Monte Carlo Methods and Applications, De Gruyter, vol. 5(1), pages 19-38, December.
    2. Eckhard Platen & Lei Shi, 2008. "On the Numerical Stability of Simulation Methods for SDES," Research Paper Series 234, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Nicola Bruti-Liberati & Eckhard Platen, 2008. "Strong Predictor-Corrector Euler Methods for Stochastic Differential Equations," Research Paper Series 222, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Bäuerle Nicole & Gilitschenski Igor & Hanebeck Uwe, 2015. "Exact and approximate hidden Markov chain filters based on discrete observations," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 159-176, December.

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    stochastic differential equations; Zakai equation; quasi-exact approximation; hidden Markov chain filtering;

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