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Stability of Feynman-Kac Formulae with Path-dependent Potentials

Author

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  • Nicolas CHOPIN

    (Crest)

  • Pierre DEL MORAL

    (Crest)

  • Sylvain RUBENTHALER

    (Crest)

Abstract

Several particle algorithms admit a Feynman-Kac representation such that the potential function may be expressed as a recursive function which depends on the complete state trajectory. An important example is the mixture Kalman filter, but other models and algorithms of practical interest fall in this category. We study the asymptotic stability of such particle algorithms as time goes to infinity. As a corollary, practical conditions for the stability of the mixture Kalman filter, and a mixture GARCH filter, are derived. Finally, we show that our results can also lead to weaker conditions for the stability of standard particle algorithms for which the potential function depends on the last state only.
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Suggested Citation

  • Nicolas CHOPIN & Pierre DEL MORAL & Sylvain RUBENTHALER, 2010. "Stability of Feynman-Kac Formulae with Path-dependent Potentials," Working Papers 2010-03, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2010-03
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    2. Whiteley, Nick & Kantas, Nikolas & Jasra, Ajay, 2012. "Linear variance bounds for particle approximations of time-homogeneous Feynman–Kac formulae," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1840-1865.

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