Stability of Feynman-Kac formulae with path-dependent potentialsReport as inadecuate




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1 CREST - Centre de Recherche en Économie et Statistique 2 ENSAE ParisTech - École Nationale de la Statistique et de l-Administration Économique 3 ALEA - Advanced Learning Evolutionary Algorithms Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251 4 JAD - Laboratoire Jean Alexandre Dieudonné

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, such that the potential function depends on the last state only.


Keywords : Feynman-Kac formulae mixture Kalman filter path-dependent potential function Particle filter





Author: Nicolas Chopin - Pierre Del Moral - Sylvain Rubenthaler -

Source: https://hal.archives-ouvertes.fr/



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