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Quasi-exact Approximation of Hidden Markov Chain Filters

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Abstract

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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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp258.pdf
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    References listed on IDEAS

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    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. G. N. Milstein & Eckhard Platen & H. Schurz, 1998. "Balanced Implicit Methods for Stiff Stochastic Systems," Published Paper Series 1998-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    3. 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.
    4. 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.
    5. P. E. Kloeden & Eckhard Platen, 1992. "Higher-order implicit strong numerical schemes for stochastic differential equations," Published Paper Series 1992-1, Finance Discipline Group, UTS Business School, 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.
    2. Nicole Bauerle & Igor Gilitschenski & Uwe D. Hanebeck, 2014. "Exact and Approximate Hidden Markov Chain Filters Based on Discrete Observations," Papers 1411.0849, arXiv.org, revised Dec 2014.
    3. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2013, January-A.

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