Stability of Feynman-Kac Formulae with Path-dependent Potentials
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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- Christophe Andrieu & Arnaud Doucet, 2002. "Particle filtering for partially observed Gaussian state space models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 827-836.
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- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Nicolas Chopin, 2007. "Dynamic Detection of Change Points in Long Time Series," Annals of the Institute of Statistical Mathematics, Springer, vol. 59(2), pages 349-366, June.
- Rong Chen & Jun S. Liu, 2000. "Mixture Kalman filters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 493-508.
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