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Issue ESAIM: Proc.
Volume 19, 2007
Conference Oxford sur les méthodes de Monte Carlo séquentielles
Page(s) 73 - 78
DOI http://dx.doi.org/10.1051/proc:071910
Published online 30 October 2007

ESAIM: Proc., 2007, Vol. 19, pp. 73-78
DOI: 10.1051/proc:071910

Stability of the discrete time filter in terms of the tails of noise distributions

Kari Heine

Institute of Mathematics, Tampere University of Technology, Finland


(Published online: 30 October 2007)

Abstract
Recently, it has been pointed out by several authors that the uniform convergence of the stochastic discrete time filter approximations, such as particle filters, is closely related to the stability of the exact filter. This work provides easily verifiable conditions on the signal and observation model that ensure a certain level of stability for the exact filter. Essentially, the conditions are imposed on the tails of the signal and observation noise distributions. For sufficiently light tailed observation noise, the filter is shown to be stable.



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