Stability of Feynman-Kac Formulae with Path-dependent Potentials
AbstractSeveral 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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Bibliographic InfoPaper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2010-03.
Date of creation: 2010
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Other versions of this item:
- Chopin, N. & Del Moral, P. & Rubenthaler, S., 2011. "Stability of Feynman-Kac formulae with path-dependent potentials," Stochastic Processes and their Applications, Elsevier, vol. 121(1), pages 38-60, January.
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