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.
(This abstract was borrowed from another version of this item.)
|Date of creation:||2010|
|Date of revision:|
|Contact details of provider:|| Postal: 15 Boulevard Gabriel Peri 92245 Malakoff Cedex|
Phone: 01 41 17 60 81
Web page: http://www.crest.fr
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2010-03. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Florian Sallaberry)
If references are entirely missing, you can add them using this form.